Strong descent numbers and Turán type theorems

Ron M. Adin; Yuval Roichman

Strong descent numbers and Turán type theorems

Department of Mathematics

Research output: Contribution to conference › Paper › peer-review

Abstract

For a permutation π in the symmetric group S _n let the total degree be its valency in the Hasse diagram of the strong Bruhat order on S _n, and let the down degree be the number of permutations which are covered by π in the strong Bruhat order. The maxima of the total degree and the down degree and their values at a random permutation are computed. Proofs involve variants of a classical theorem of Turán from extremal graph theory.

Original language	English
Pages	338-345
Number of pages	8
State	Published - 2006
Event	18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006 - San Diego, CA, United States Duration: 19 Jun 2006 → 23 Jun 2006

Conference

Conference	18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006
Country/Territory	United States
City	San Diego, CA
Period	19/06/06 → 23/06/06

Keywords

Bruhat order
Descent number
Symmetric group
Turan graph

Cite this

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title = "Strong descent numbers and Tur{\'a}n type theorems",

abstract = "For a permutation π in the symmetric group S n let the total degree be its valency in the Hasse diagram of the strong Bruhat order on S n, and let the down degree be the number of permutations which are covered by π in the strong Bruhat order. The maxima of the total degree and the down degree and their values at a random permutation are computed. Proofs involve variants of a classical theorem of Tur{\'a}n from extremal graph theory.",

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author = "Adin, {Ron M.} and Yuval Roichman",

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AU - Roichman, Yuval

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N2 - For a permutation π in the symmetric group S n let the total degree be its valency in the Hasse diagram of the strong Bruhat order on S n, and let the down degree be the number of permutations which are covered by π in the strong Bruhat order. The maxima of the total degree and the down degree and their values at a random permutation are computed. Proofs involve variants of a classical theorem of Turán from extremal graph theory.

AB - For a permutation π in the symmetric group S n let the total degree be its valency in the Hasse diagram of the strong Bruhat order on S n, and let the down degree be the number of permutations which are covered by π in the strong Bruhat order. The maxima of the total degree and the down degree and their values at a random permutation are computed. Proofs involve variants of a classical theorem of Turán from extremal graph theory.

KW - Bruhat order

KW - Descent number

KW - Symmetric group

KW - Turan graph

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T2 - 18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006

Y2 - 19 June 2006 through 23 June 2006

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Strong descent numbers and Turán type theorems

Abstract

Conference

Keywords

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