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Generalized Noncrossing Partitions And Combinatorics Of Coxeter Groups by Drew Armstrong

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1Generalized Noncrossing Partitions And Combinatorics Of Coxeter Groups

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This memoir constitutes the author's PhD thesis at Cornell University. It serves both as an expository work and as a description of new research. At the heart of the memoir, we introduce and study a poset $NC^{(k)}(W)$ for each finite Coxeter group $W$ and for each positive integer $k$. When $k=1$, our definition coincides with the generalized noncrossing partitions introduced by Brady-Watt and Bessis. When $W$ is the symmetric group, we obtain the poset of classical $k$-divisible noncrossing partitions, first studied by Edelman. Along the way, we include a comprehensive introduction to related background material. Before defining our generalization $NC^{(k)}(W)$, we develop from scratch the theory of algebraic noncrossing partitions $NC(W)$. This involves studying a finite Coxeter group $W$ with respect to its generating set $T$ of {\em all} reflections, instead of the usual Coxeter generating set $S$. This is the first time that this material has appeared in one place. Finally, it turns out that our poset $NC^{(k)}(W)$ shares many enumerative features in common with the ``generalized nonnesting partitions'' of Athanasiadis and the ``generalized cluster complexes'' of Fomin and Reading. In particular, there is a generalized ``Fuss-Catalan number'', with a nice closed formula in terms of the invariant degrees of $W$, that plays an important role in each case. We give a basic introduction to these topics, and we describe several conjectures relating these three families of ``Fuss-Catalan objects''.

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  • Title: ➤  Generalized Noncrossing Partitions And Combinatorics Of Coxeter Groups
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 73.67 Mbs, the file-s for this book were downloaded 172 times, the file-s went public at Wed Sep 18 2013.

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1Teacup Club (Dramatic Reading)

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The Teacup Club (For the Advancement of Woman) is formed when Dorothy decides to found an intellectual club of her own - to teach her fiance a lesson! The club’s discussion topics (official) includes Theosophy, Politics and Women in Legislature. The club’s unofficial topics include Emily’s new dress, man-flu (it's causes and cures) and the great mystery of the missing chafing-dish. A witty drama and a comedy of manners, secrets and politics (both official and unofficial). - Summary by Elizabby <br><br><b>Cast List:</b><br><br> <b>Cast</b><br/> Narrator: <a href="https://librivox.org/reader/6281">Beth Thomas</a><br/> Evelyn: <a href="https://librivox.org/reader/10494">Jennifer Fournier</a><br/> Emily: <a href="https://librivox.org/reader/10614">Leanne Yau</a><br/> Dorothy: <a href="https://librivox.org/reader/8677">KHand </a><br/> Frances: <a href="https://librivox.org/reader/6281">Beth Thomas</a><br/> Elise: <a href="https://librivox.org/reader/8883">Lydia </a><br/> Marion: <a href="https://librivox.org/reader/11109">Vicki Hibbins</a><br/> Catharine: <a href="https://librivox.org/reader/7026">Michele Eaton</a><br/><br/> <b>Edited by:</b> <a href="https://librivox.org/reader/7026">Michele Eaton</a> and <a href="https://librivox.org/reader/5796">linny </a><br></br> <b>Proof listeners:</b> <a href="https://librivox.org/reader/7026">Michele Eaton</a>, <a href="https://librivox.org/reader/6281">Beth Thomas</a>

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  • Number of Sections: 12
  • Total Time: 04:20:40

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2Postage stamps of war (1854-1914)

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A very brief introduction to postal stamps used and issued during times of war. The principal focus might be said to be placed upon the Great War which just erupted in Europe and across much of the globe. - Summary by KevinS

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  • Title: ➤  Postage stamps of war (1854-1914)
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  • Number of Sections: 3
  • Total Time: 01:21:10

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