A crystal-like structure on shifted tableaux

Diagonal Vectors of Shifted Young Tableaux

X iv :0 80 3. 22 53 v2 [ m at h. C O ] 4 F eb 2 00 9 DIAGONAL VECTORS OF SHIFTED YOUNG TABLEAUX DORIAN CROITORU Abstra t. We study ve tors formed by entries on the diagonal of standard Young tableaux of shifted shapes. Su h ve tors are in bije tion with integer latti e points of ertain integral polytopes, whi h are Minkowski sums of simpli es. We also des ribe verti es of these polytopes, and o...

Bumping algorithm for set-valued shifted tableaux

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...

Swiching Rule on the Shifted Rim Hook Tableaux

When the Schur function sλ corresponding to a partition λ is defined as the generating function of the column strict tableaux of shape λ it is not at all obvious that sλ is symmetric. In [BK] Bender and Knuth showed that sλ is symmetric by describing a switching rule for column strict tableaux, which is essentially equivalent to the jeu de taquin of Schützenberger (see [Sü]). Bender and Knuth’s...

Crystal Bases and Young Tableaux

Triangle-Free Triangulations, Hyperplane Arrangements and Shifted Tableaux

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...