Geodesic
On Degrees in the Hasse Diagram of the Strong Bruhat Order
Séminaire lotharingien de combinatoire, Tome 53 (2005-2006)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

For a permutation \pi in the symmetric group Sn let the total degree be its valency in the Hasse diagram of the strong Bruhat order on Sn, and let the down degree be the number of permutations which are covered by \pi 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. 

@article{SLC_2005-2006_53_a6,
     author = {Ron M. Adin and Yuval Roichman},
     title = {On {Degrees} in the {Hasse} {Diagram} of the {Strong} {Bruhat} {Order}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {53},
     year = {2005-2006},
     url = {http://geodesic.mathdoc.fr/item/SLC_2005-2006_53_a6/}
}
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Ron M. Adin; Yuval Roichman. On Degrees in the Hasse Diagram of the Strong Bruhat Order. Séminaire lotharingien de combinatoire, Tome 53 (2005-2006). http://geodesic.mathdoc.fr/item/SLC_2005-2006_53_a6/