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On Degrees in the Hasse Diagram of the Strong Bruhat Order

Ron M. Adin·Yuval Roichman
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Abstract

For a permutation $π$ in the symmetric group $S_n$ let the {\it total degree} be its valency in the Hasse diagram of the strong Bruhat order on $S_n$, and let the {\it 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.

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Ron M. Adin, Yuval Roichman. 2006-03-12. On Degrees in the Hasse Diagram of the Strong Bruhat Order. https://arxiv.org/abs/math/0505020

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