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In a recent article (arXiv:1507.03499) (joint with Alon Regev) we studied sums of squares of characters Chi(L,M) of the Symmetric Group over shapes L that are two-rowed, and shapes L that are hook shapes, and M is an arbitrary shape that mostly consists of ones, and designed algorithms for closed-form evaluations of each of these. We noted (and proved) that when M is the shape with n cells consisting of 3 followed by n-3 ones, the former sum equals one half time the analogous sum over hook shapes with n+2 cells and M is the partition consisting of 3,2, followed by n-3 ones. Here we show that this is just a tip of an iceberg, and prove (alas, by purely human means) that the former sum with M consisting of all odd parts, and (possibly) a consecutive string of powers of 2, starting at 2, equals one half of the latter sum where M is replaced by a partition where all the odd parts are retained but the consecutive string of powers of 2: 2,4, ..., $2^{t-1}$ is replaced by $2^t$.

31 pages : 28 cm

31 pages : 28 cm

31 pages : 28 cm

Wrote a small file in C4D which Makes L Shapes Parts of Lego from Open Cad STL files there are some of the Results Also Made a better Naming System for my Parts

Wrote a small file in C4D which Makes L Shapes Parts of Lego from Open Cad STL files there are some of the Results Also Made a better Naming System for my Parts

Wrote a small file in C4D which Makes L Shapes Parts of Lego from Open Cad STL files there are some of the Results Also Made a better Naming System for my Parts

Wrote a small file in C4D which Makes L Shapes Parts of Lego from Open Cad STL files there are some of the Results Also Made a better Naming System for my Parts

Wrote a small file in C4D which Makes L Shapes Parts of Lego from Open Cad STL files there are some of the Results Also Made a better Naming System for my Parts

p. cm

As babies develop, their understanding of the world, and how its pieces "fit" together, continues to progress. Discovering Shapes playfully introduces five basic forms circle, oval, triangle, square and rectangle as each appears in the context of toys, nature and everyday objects. We've added adorable puppet shows; silly sound effects; happy, busy babies and captivating real-world imagery accompanied by beautiful classical music to provide a delightful sensory experience. So whether your baby plays along by bouncing a ball, watching eggs hatch, building with blocks, or tracing the outline of a checkerboard, you'll enjoy sharing in that fresh sense of wonder that takes shape as your child greets each new discovery! BONUS EXTRAS: • Repeat Play • Discovery Cards • Story Time with See and Spy Shapes • Puppet Shows • Locate The Shape • Toy Chest You are provided with two downloading options: 1) An H.264-derived version of the entire contents, letting you watch it whenever and wherever you go. 2) The ISO file, containing the complete disc contents. Burn it to a blank DVD disc to watch it on your big-screen TV or mount it on your computer in conjunction with software such as VLC Media Player to watch it on your computer (different playback devices and/or computers may produce different results). Aspect Ratio: 1.33:1 (Full Screen) Audio: Dolby 2.0: American English, Canadian French, Latin Spanish Subtitles: English for the hearing-impaired English closed-captioning for the hearing-impaired Menu Language: English Dual-Layer Format (DVD-9): Transition between DVD layers may trigger a slight pause

As babies develop, their understanding of the world, and how its pieces "fit" together, continues to progress. Discovering Shapes playfully introduces five basic forms circle, oval, triangle, square and rectangle as each appears in the context of toys, nature and everyday objects. We've added adorable puppet shows; silly sound effects; happy, busy babies and captivating real-world imagery accompanied by beautiful classical music to provide a delightful sensory experience. So whether your baby plays along by bouncing a ball, watching eggs hatch, building with blocks, or tracing the outline of a checkerboard, you'll enjoy sharing in that fresh sense of wonder that takes shape as your child greets each new discovery! BONUS EXTRAS: • Repeat Play • Discovery Cards • Story Time with See and Spy Shapes • Puppet Shows • Locate The Shape • Toy Chest You are provided with two downloading options: 1) An H.264-derived version of the entire contents, letting you watch it whenever and wherever you go. 2) The ISO file, containing the complete disc contents. Burn it to a blank DVD disc to watch it on your big-screen TV or mount it on your computer in conjunction with software such as VLC Media Player to watch it on your computer (different playback devices and/or computers may produce different results). Aspect Ratio: 1.33:1 (Full Screen) Audio: Dolby 2.0: American English, Canadian French, Latin Spanish Subtitles: English for the hearing-impaired English closed-captioning for the hearing-impaired Menu Language: English Dual-Layer Format (DVD-9): Transition between DVD layers may trigger a slight pause

As babies develop, their understanding of the world, and how its pieces "fit" together, continues to progress. Discovering Shapes playfully introduces five basic forms circle, oval, triangle, square and rectangle as each appears in the context of toys, nature and everyday objects. We've added adorable puppet shows; silly sound effects; happy, busy babies and captivating real-world imagery accompanied by beautiful classical music to provide a delightful sensory experience. So whether your baby plays along by bouncing a ball, watching eggs hatch, building with blocks, or tracing the outline of a checkerboard, you'll enjoy sharing in that fresh sense of wonder that takes shape as your child greets each new discovery! BONUS EXTRAS: • Repeat Play • Discovery Cards • Story Time with See and Spy Shapes • Puppet Shows • Locate The Shape • Toy Chest You are provided with two downloading options: 1) An H.264-derived version of the entire contents, letting you watch it whenever and wherever you go. 2) The ISO file, containing the complete disc contents. Burn it to a blank DVD disc to watch it on your big-screen TV or mount it on your computer in conjunction with software such as VLC Media Player to watch it on your computer (different playback devices and/or computers may produce different results). Aspect Ratio: 1.33:1 (Full Screen) Audio: Dolby 2.0: American English, Canadian French, Latin Spanish Subtitles: English for the hearing-impaired English closed-captioning for the hearing-impaired Menu Language: English Dual-Layer Format (DVD-9): Transition between DVD layers may trigger a slight pause

As babies develop, their understanding of the world, and how its pieces "fit" together, continues to progress. Discovering Shapes playfully introduces five basic forms circle, oval, triangle, square and rectangle as each appears in the context of toys, nature and everyday objects. We've added adorable puppet shows; silly sound effects; happy, busy babies and captivating real-world imagery accompanied by beautiful classical music to provide a delightful sensory experience. So whether your baby plays along by bouncing a ball, watching eggs hatch, building with blocks, or tracing the outline of a checkerboard, you'll enjoy sharing in that fresh sense of wonder that takes shape as your child greets each new discovery! BONUS EXTRAS: • Repeat Play • Discovery Cards • Story Time with See and Spy Shapes • Puppet Shows • Locate The Shape You are provided with two downloading options: 1) An H.264-derived version of the entire contents, letting you watch it whenever and wherever you go. 2) The ISO file, containing the complete disc contents. Burn it to a blank DVD disc to watch it on your big-screen TV or mount it on your computer in conjunction with software such as VLC Media Player to watch it on your computer (different playback devices and/or computers may produce different results). Aspect Ratio: 1.33:1 (Full Screen) Audio: Dolby 2.0: Spain Spanish, Catalan, American English, European Portuguese Dual-Layer Format (DVD-9): Transition between DVD layers may trigger a slight pause

As babies develop, their understanding of the world, and how its pieces "fit" together, continues to progress. Discovering Shapes playfully introduces five basic forms circle, oval, triangle, square and rectangle as each appears in the context of toys, nature and everyday objects. We've added adorable puppet shows; silly sound effects; happy, busy babies and captivating real-world imagery accompanied by beautiful classical music to provide a delightful sensory experience. So whether your baby plays along by bouncing a ball, watching eggs hatch, building with blocks, or tracing the outline of a checkerboard, you'll enjoy sharing in that fresh sense of wonder that takes shape as your child greets each new discovery! BONUS EXTRAS: • Repeat Play • Discovery Cards • Story Time with See and Spy Shapes • Puppet Shows • Locate The Shape You are provided with two downloading options: 1) An H.264-derived version of the entire contents, letting you watch it whenever and wherever you go. 2) The ISO file, containing the complete disc contents. Burn it to a blank DVD disc to watch it on your big-screen TV or mount it on your computer in conjunction with software such as VLC Media Player to watch it on your computer (different playback devices and/or computers may produce different results). Aspect Ratio: 1.33:1 (Full Screen) Audio: Dolby 2.0: Spain Spanish, Catalan, American English, European Portuguese Dual-Layer Format (DVD-9): Transition between DVD layers may trigger a slight pause

Sources: - Discovering Shapes 2007 US DVD - World of Rhythm 2011 US DVD

Sources: - Discovering Shapes 2007 US DVD - World of Rhythm 2011 US DVD

1Lady's Life on a Farm in Manitoba

By Mary Georgiana Caroline Hall

In 1881, Mrs. Cecil Hall's brother went to Manitoba to farm. In 1882, she went out for a visit of some two months, and followed that visit with a long sojourn in Colorado, returning to England as the snows began to fall. While there, she had to give up her "Lady's ways" and help on the farm in many ways she'd never stoop to at home. She makes hay, cooks, paints the barn roof, and cleans. Through it all, the newness helped her keep her temper, and these letters home show an insight into the settlement of Western Canada. These letters have a feel of "Little House on the Prairie" from an English lady's point of view. (Summary by Sibella Denton).

2Kitchener's Mob Adventures of an American in the British Army

By James Norman Hall

“Pvt Ryan”, “Platoon”, “A Soldier’s Home”, Kitchener’s Mob”. These aren’t happy stories, they are about the experience of War. War at different times, and although modern warfare may be more sanitized, the adventure, the horror, the emotions don’t change. James Norman Hall has been there. He “Saw the Elephant”, and his portrayal of his WWI experience is a tribute to those ordinary people who do such extraordinary things.<BR><BR> Those who have served will identify with at least some part if not all of this book, be it the rigors of training, the camaraderie, or possibly those memories that try as you may, you can never make go away. Those who haven’t may gain insight and possibly more respect for those who have.<BR><BR> Tommy Atkins is a universal soldier, be he the cook that serves up a hot meal, the sniper that keeps score on the stock of his rifle, or the machine gunner who hates his job. As I narrated this book, I had to stop and compose myself more than once. I could almost feel Hall’s presence as we told Tommy’s story.<BR><BR> Mike Vendetti, Narrator<BR> 2 Lt Inf Vietnam 1965

3High Adventure A Narrative of Air Fighting in France

By James Norman Hall

High Adventure A Narrative of Air Fighting in France by James Norman Hall; you will find this book although an exciting narrative has an unpolished feel because it was published in June of 1918 while Mr. Hall was a captive in a German POW camp. When he was captured behind enemy lines, the book was still a work in progress. The Armistice would not be reached until November of that year.<br /><br />Although he does not mention it in this book, Mr. Hall had already served the better part of 15 months with the British Expeditionary Forces, surviving the battle of Loos in Sept – Oct 1915, and upon which his excellent work “Kitchener’s” Mob is Based.<br /><br />The US did not enter the war until April 1917, and Hall had already served nearly three years as an American with British and French forces, as a machine gunner with the British, and as a pilot in the Lafayette Escadrille.<br /><br />Pilot training in the French Air Corps was primarily a matter of survival. Visualize if you will, a class of “Penguins”, aircraft with wings too short for flight scurrying about the airfield as student pilots learn to control these machines with no instructor on board, and for that matter in Mr. Halls case there was never an instructor on board. Their solo flight was their first flight. They learned by doing.<br /><br />The sheer joy and wonder of man’s early experience of leaving the bounds of Earth in an aircraft coupled with the danger and excitement of air combat made “High Adventure” such a good read, I completed the narration ahead of schedule, because I couldn’t put it down<br /><br />Mike Vendetti, Narrator

Returning from the horrors of World War I James Hall and Charles Nordhoff follow a dream to tour the South Pacific. They later co authored “Mutiny on the Bounty”. This is a love story. A travelogue and an adventure rolled into one. This book just went into the public domain, so enjoy an early 20th Century look at paradise. (Summary by Mike Vendetti)

5Viking Tales

By Jennie Hall

Viking tales are tales from Iceland, featuring the king Halfdan and his son Harald. (Summary by Nadine)

6Untroubled Mind

By Herbert J. Hall

A very wise physician has said that “every illness has two parts—what it is, and what the patient thinks about it.” What the patient thinks about it is often more important and more troublesome than the real disease. What the patient thinks of life, what life means to him is also of great importance and may be the bar that shuts out all real health and happiness. The following pages are devoted to certain ideals of life which I would like to give to my patients, the long-time patients who have especially fallen to my lot. (Summary by Herbert J Hall - from the Preface)

7Treatise on Staff Making and Pivoting

By Eugene Edward Hall

This instruction manual contains complete directions for making and fitting new staffs for watches from raw material. The author refers to several illustrations throughout the text. These can be seen at the Online text in the Links section on this page. (Bev J. Stevens)

8Love Romances of the Aristocracy

By Thornton Hall

There are countless romances set in the British upper class, but the hearts of the real-life counterparts of the fictional heroes have also been conquered, lost, or broken. The real peerage has lived through romances and scandals as outrageous as their fictional cousins, and this book is sharing all the gossip about those adventures. - Summary by Carolin

9Astounding Stories 14, February 1931

By Harry Bates, Charles Willard Diffin, Anthony Gilmore, Desmond Winter Hall, F. V. W. Mason and Captain S. P. Meek

This issue includes "Werewolves of War" by D. W. Hall, "The Tentacles from Below" by Anthony Gilmore, "The Black Lamp" by Captain S. P. Meek, "Phalanxes of Atlans" by F. V. W. Mason, and continues with "The Pirate Planet" by Charles W. Diffin, - Summary by Bill Boerst

As the story begins, title character Grace Ingalis is a young woman with a middle-class socialite's upbringing who decides to marry a well-off young businessman she met mere weeks before on a winter sail to the West Indies. But intrigue is brewing as her married (and quite jealous) older sister Lydia is feeling left out, and a religious awakening awaits Grace. The story is reminiscent of Edith Wharton, who was a family friend, by way of Hall's art critic husband, Mr. Brownell. - Summary by BellonaTimes

11'Twixt Earth and Stars

By Radclyffe Hall

This is a volume of poetry by Radclyffe Hall. The poet and novelist led a highly scandalous lifestyle for the norms of her contemporary society, living openly lesbian in Germany and England. Some of the poems in this volume are also love poems to other women, a fact which was not generally known at the time the book was published. - Summary by Carolin

12Sheaf of Verses

By Radclyffe Hall

This is a volume of poetry by Radclyffe Hall. At the time of publication of this novel, Radclyffe Hall was living in Bad Homburg in Germany, in a lesbian relationship. Some of the poems in this volume are love poems, and to spare the public's delicate sensibilities, the names of the people to whom the poems were dedicated are removed. - Summary by Carolin

13Love Affairs of the Courts of Europe

By Thornton Hall

The best stories are written by life itself, and that is why Thornton Hall has collected real life love stories in this volume. All the Princes Charming and the Fair Maidens of these stories are historical figures, which have at one time played their roles at one of the many Courts of Europe. Hall's writing style is entertaining and easy to follow, and though he may be guilty of embellishing the stories, the flourishes only add to their charm. - Summary by Carolin

14Untroubled Mind (Version 2)

By Herbert J. Hall

Our own minds cause us great pain through worry, fear and anxiety. We all know this, but how to stop the whirling, spinning wheel inside our heads? How to calm our racing thoughts and reach a truly untroubled mind? This medical doctor shares his wisdom about this gathered in years of practice and research. It is well worth listening to."When a man tells me he never worries, I am inclined to think that he is either deceiving himself or trying to deceive me. The great roots of worry are conscience, fear, and regret. Undoubtedly we ought to be conscientious and we ought to fear and regret evil. But if it is to be better than an impediment and a harm, our worry must be largely unconscious, and intuitive. The moment we become conscious of worry we are undone.... The remedy for the mental unrest, which is in itself an illness, lies not in an enlightened knowledge of the harmfulness and ineffectiveness of worry, not even in the acquirement of an unconscious conscience, but in the living of a life so full and good that worry cannot find place in it." - Summary by the author

Henry Martyn (1781-1812), a brilliant and ambitious young student in Cambridge, England, was led by God to be a missionary to India and Persia. While pastoring, starting schools, and teaching the locals as well as Europeans through his role as chaplain for the East India Company, he worked on several far-reaching Bible translations. All this despite much weakness and illness due to harsh climates and difficult travels. This short life of 31 years is a testament to the power of God to work through one life fully dedicated to Him. (Summary by HannahMary)

16Mother Earth, Vol. 1 No. 1, March 1906

By Max Baginski, Edwin Bjorkman, Frances Maule Bjorkman, John Russell Coryell, Emma Goldman, Maxim Gorky, Bolton Hall, Harry May Kelly and Grace Potter

"Mother Earth was an American anarchist journal that described itself as "A Monthly Magazine Devoted to Social Science and Literature". Founded in early 1906 and initially edited by Emma Goldman, an activist in the United States, it published articles by contemporary activists and writers in Europe as well as the US, in addition to essays by historic figures." This is Volume 1 of the series - Summary by Wikepedia

17Viking Tales (Version 2)

By Jennie Hall

The story follows the life of the Viking Harald from infancy to his crowning as King of Norway. It focuses on the Vikings' eagerness for adventure and new lands as they set forth from Norway and sail westward across the Atlantic, island-hopping on their way to America. The legends of these men were passed down through generations of families, while they sat around the fireside on bitterly cold winter nights playing harps and working with wool. This adventurous book will entertain young and old readers alike as they take a look at the lifestyle and world view of these mysterious people.

In this tome the Northern narrator, Harold Edson, visits the American South with his college friend, Stanton White, in order to study first hand the social conditions of African Americans during the post-reconstruction era. Edson describes encounters with racist whites whose attacks on African Americans are vicious and unrepentant. <br><br> This narrative reflects primitive ideas about race that prevailed in the 19th century United States--above and below the Mason-Dixon--and a level of ignorance that, to a 21st century listener, may be difficult to fully appreciate. But in fact, many of the notions Hall visits in the text continue to echo today reminding us that race has always been a foundation upon which this country was built. (Summary by James K. White)

What is it about that old house down the road that bothers Pierre and his wife Annette so much? The owners, Eric and Julia, seem like nice people, but there's an aura of evil permeating the place. Why does Eric exude a supernatural malevolence about him wherever he goes? Eric and Julia look as much in love as anyone Pierre has ever seen, yet Julia's body is covered with mysterious injuries. Can Eric really be the cause or is something far more terrifying at work? (Summary by Ben Tucker)

20Initiates of the Flame

By Manly P. Hall

A book about the spiritual flame that nourishes all created things and the initiates who guard it. It explores the mysteries of alchemy, Egypt, the Grail, and the pyramids through the eyes of a mystic philosopher.

James Hall was a soldier, lawyer, circuit judge, newspaper editor, historian, and author of fiction. He was also the first publisher of a literary magazine west of Pittsburgh. Hall originally wrote some of the letters in this collection in 1820, while voyaging by keelboat down the Ohio River from Pittsburgh to Shawneetown, Illinois, where he established a law practice. He appears to have revised the 1820 letters and added more prior to publication in London in 1828. Much more than a description of his travels, the letters include his observations on many subjects, reflecting current affairs and his broad interests. Topics include: Cumberland Road; Internal Improvements in 1820s; Harman Blennerhassett; Burr's Conspiracy; Manners of the People in Old Northwest; General Presby Neville; Cincinnati in 1820s; Arthur St. Clair; Falls of the Ohio; Shawneetown Illinois; Backwoodsmen; Daniel Boone; Harpe Brothers; Regulators; Popular superstitions Ohio River Valley. - Summary by Ted Lienhart

This collection of strange and exotic stories offers adaptations and modern updates of folk tales and legends as well as original horror stories involving the mysterious secrets of the Orient. - Summary by Ben Tucker

23Three Acres and Liberty

By Bolton Hall

It (this book) shows what is needed for a city man or woman to support a family on the proceeds of a little bit of land; it shows how in truth, as the old Book prophesied, the earth brings forth abundantly after its kind to satisfy the desire of every living thing. It is not necessary to bury oneself in the country, nor, with the new facilities of transportation, need we, unless we wish to, pay the extravagant rents and enormous cost of living in the city. A little bit of land near the town or the city can be rented or bought on easy terms; and merchandising will bring one to the city often enough. Neither is hard labor needed; but it is to work alone that the earth yields her increase, and if, although unskilled, we would succeed in gardening, we must attend constantly and intelligently to the home acres. - Summary by Bolton Hall

24Well Of Loneliness

By Radclyffe Hall

The story of Stephen Gordon, a girl born in the late 19th century into a privileged English family. She knows from an early age that she is different to other children and the story deals with her struggles over her sexual orientation and the challenges for lesbians in society. - Summary by Hazel Moon