Free Action and Cyclic Sieving on Skew Semi-standard Young Tableaux

Enumeration of Semi { Standard Young Tableaux

Standard tableaux. A Young tableau (also known as a standard tableau) is an arrangement of distinct integers in an array of left justiied rows, such that the entries of each row are in increasing order from left to right and the entries of each column are in increasing order from bottom to top 2. For instance, here is an array of size 15: 11 4 8 12 14 3 6 7 13 1 2 5 9 10 15 : In general a table...

On the Enumeration of Skew Young Tableaux

Cyclic sieving of increasing tableaux and small Schröder paths

An increasing tableau is a semistandard tableau with strictly increasing rows and columns. It is well known that the Catalan numbers enumerate both rectangular standard Young tableaux of two rows and also Dyck paths. We generalize this to a bijection between rectangular 2-row increasing tableaux and small Schröder paths. Using the jeu de taquin for increasing tableaux of [Thomas–Yong ’09], we t...

Virasoro action on Schur function expansions, skew Young tableaux and random walks

5 The action of Virasoro on Schur polynomials 31 Department of Mathematics, Brandeis University, Waltham, Mass 02454, USA. Email: [email protected]. The support of a National Science Foundation grant # DMS01-00782 is gratefully acknowledged. Department of Mathematics, Université de Louvain, 1348 Louvain-la-Neuve, Belgium and Clay Mathematics Institute, One Bow Street, Cambridge, MA 02138, USA....

Hopf Structures on Standard Young Tableaux

We review the Poirier-Reutenauer Hopf structure on Standard Young Tableaux and show that it is a distinguished member of a family of Hopf structures. The family in question is related to deformed parastatistics. In this paper K is a field of characteristic zero and all vector spaces are over K. A K[S]-module is a collection of K[Sr]-modules of the symmetric groups Sr. A H(q)-module is a collect...