We give a basis of bideterminants for the coordinate ring K[O(n)] of the orthogonal group O(n, K), where K is an infinite field of characteristic not 2. The bideterminants are indexed by pairs of Young tableaux which are O(n)-standard in the sense of King-Welsh. We also give an explicit filtration of K[O(n)] as an O(n, K)-bimodule, whose factors are isormorphic to the tensor product of orthogon...

Flips of diagonals in colored triangle-free triangulations of a convex polygon are interpreted as moves between two adjacent chambers in a certain graphic hyperplane arrangement. Properties of geodesics in the associated flip graph are deduced. In particular, it is shown that: (1) every diagonal is flipped exactly once in a geodesic between distinguished pairs of antipodes; (2) the number of ge...

For any fixed integer d≥ 1, let ud(N) denote the number of permutations in the symmetric group S(N)which have no decreasing subsequence of length d+1.Regev determined the asymptotic form of ud(N) in the N→ ∞ limit; his argument relies on Selberg’s integral formula. In this article we give an elementary derivation of Regev’s formula via an asymptotic bijection with standard Young tableaux of rec...

This paper presents a combinatorial study of the super plactic monoid type A, which is related to representations general linear Lie superalgebra. We introduce analogue Schützenberger’s jeu de taquin on structure tableaux over signed alphabet. show that this procedure transforms skew into Young compatible with congruence and it confluent. deduce properties relating insertion algorithms tableaux...

We derive new results for the number of star and watermelon configurations of vicious walkers in the presence of an impenetrable wall by showing that these follow from standard results in the theory of Young tableaux, and combinatorial descriptions of symmetric functions. For the problem of n-friendly walkers, we derive exact asymptotics for the number of stars and watermelons both in the absen...

We show that the quantum straightening algorithm for Young tableaux and Young bitableaux reduces in the crystal limit q 7 ! 0 to the Robinson-Schensted algorithm.

We present an insertion algorithm of Robinson–Schensted type that applies to set-valued shifted Young tableaux. Our algorithm is a generalization of both set-valued non-shifted tableaux by Buch and non set-valued shifted tableaux by Worley and Sagan. As an application, we obtain a Pieri rule for a K-theoretic analogue of the Schur Q-functions. Résumé Nous présentons un algorithme d’insertion de...