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Combinatorics Of Finite Sets by Anderson%2c Ian Ph. D.

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1Finite And Infinite Combinatorics In Sets And Logic : [proceedings Of The NATO Advanced Study Institute On Finite And Infinite Combinatorics In Sets And Logic, Banff, Alberta, Canada, April 21-May 4, 1991]

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“Finite And Infinite Combinatorics In Sets And Logic : [proceedings Of The NATO Advanced Study Institute On Finite And Infinite Combinatorics In Sets And Logic, Banff, Alberta, Canada, April 21-May 4, 1991]” Metadata:

  • Title: ➤  Finite And Infinite Combinatorics In Sets And Logic : [proceedings Of The NATO Advanced Study Institute On Finite And Infinite Combinatorics In Sets And Logic, Banff, Alberta, Canada, April 21-May 4, 1991]
  • Author: ➤  
  • Language: English

“Finite And Infinite Combinatorics In Sets And Logic : [proceedings Of The NATO Advanced Study Institute On Finite And Infinite Combinatorics In Sets And Logic, Banff, Alberta, Canada, April 21-May 4, 1991]” Subjects and Themes:

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The book is available for download in "texts" format, the size of the file-s is: 1199.13 Mbs, the file-s for this book were downloaded 38 times, the file-s went public at Thu Sep 12 2019.

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2Combinatorics Of Finite Sets

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  • Title: Combinatorics Of Finite Sets
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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: 692.89 Mbs, the file-s for this book were downloaded 494 times, the file-s went public at Tue Jul 30 2019.

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3Formalization Of Some Central Theorems In Combinatorics Of Finite Sets

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We present fully formalized proofs of some central theorems from combinatorics. These are Dilworth's decomposition theorem, Mirsky's theorem, Hall's marriage theorem and the Erd\H{o}s-Szekeres theorem. Dilworth's decomposition theorem is the key result among these. It states that in any finite partially ordered set (poset), the size of a smallest chain cover and a largest antichain are the same. Mirsky's theorem is a dual of Dilworth's decomposition theorem, which states that in any finite poset, the size of a smallest antichain cover and a largest chain are the same. We use Dilworth's theorem in the proofs of Hall's Marriage theorem and the Erd\H{o}s-Szekeres theorem. The combinatorial objects involved in these theorems are sets and sequences. All the proofs are formalized in the Coq proof assistant. We develop a library of definitions and facts that can be used as a framework for formalizing other theorems on finite posets.

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  • Title: ➤  Formalization Of Some Central Theorems In Combinatorics Of Finite Sets
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The book is available for download in "texts" format, the size of the file-s is: 0.21 Mbs, the file-s for this book were downloaded 20 times, the file-s went public at Sat Jun 30 2018.

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4Hypergraphs : Combinatorics Of Finite Sets

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We present fully formalized proofs of some central theorems from combinatorics. These are Dilworth's decomposition theorem, Mirsky's theorem, Hall's marriage theorem and the Erd\H{o}s-Szekeres theorem. Dilworth's decomposition theorem is the key result among these. It states that in any finite partially ordered set (poset), the size of a smallest chain cover and a largest antichain are the same. Mirsky's theorem is a dual of Dilworth's decomposition theorem, which states that in any finite poset, the size of a smallest antichain cover and a largest chain are the same. We use Dilworth's theorem in the proofs of Hall's Marriage theorem and the Erd\H{o}s-Szekeres theorem. The combinatorial objects involved in these theorems are sets and sequences. All the proofs are formalized in the Coq proof assistant. We develop a library of definitions and facts that can be used as a framework for formalizing other theorems on finite posets.

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  • Title: ➤  Hypergraphs : Combinatorics Of Finite Sets
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  • Language: eng,fre

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The book is available for download in "texts" format, the size of the file-s is: 394.01 Mbs, the file-s for this book were downloaded 126 times, the file-s went public at Sat Jan 28 2023.

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