In this paper we classify all Schur functions and skew Schur functions that are multiplicity free when expanded in the basis of fundamental quasisymmetric functions, termed F-multiplicity free. Combinatorially, this is equivalent to classifying all skew shapes whose standard Young tableaux have distinct descent sets. We then generalize our setting, and classify all F-multiplicity free quasisymm...

The k-Schur functions were first introduced by Lapointe, Lascoux and Morse [18] in the hopes of refining the expansion of Macdonald polynomials into Schur functions. Recently, an alternative definition for k-Schur functions was given by Lam, Lapointe, Morse, and Shimozono [17] as the weighted generating function of starred strong tableaux which correspond with labeled saturated chains in the Br...

The cactus group acts on the set of standard Young tableaux a given shape by (partial) Schützenberger involutions. It is natural to extend this action corresponding Specht module identifying with Kazhdan–Lusztig basis. We term these representations “Schützenberger modules”, denoted S Sch λ , and in paper we investigate their decomposition into irreducible components. prove that when hook shape,...

We derive new combinatorial identities which may be viewed as multivariate analogs of summation formulas for hypergeometric series. As in the previous paper Re], we start with probability distributions on the space of the innnite Young tableaux. Then we calculate the probability that the entry of a random tableau at a given box equals n = 1; 2; : : :. Summing these probabilities over n and equa...

Let X, Y be finite sets and T a set of functions from X → Y which we will call “tableaux”. We define a simplicial complex whose facets, all of the same dimension, correspond to these tableaux. Such tableau complexes have many nice properties, and are frequently homeomorphic to balls, which we prove using vertex decompositions [BP79]. In our motivating example, the facets are labeled by semistan...

We define P-strict labelings for a finite poset P as generalization of semistandard Young tableaux and show that promotion on these objects is in equivariant bijection with toggle action B-bounded Q-partitions an associated Q. In many nice cases, this conjugate to rowmotion. apply result flagged tableaux, Gelfand-Tsetlin patterns, symplectic obtaining new cyclic sieving homomesy conjectures. al...

We compute the dimension of some irreducible representations of the sym­ metric groups in characteristic ρ (Theorem 2). The representations considered here are associated with Young diagrams m : πΐχ > m 2 > ... > m/ such that πΐχ — mi < (jp — I). The formula is based on a variant of Verlinde's formula which computes some tensor product multiplicities of indecomposable modules for GLi(¥p), as it...

We suggest an approach for the enumeration of minimal permutations having d descents which uses skew Young tableaux. We succeed in finding a general expression for the number of such permutations in terms of (several) sums of determinants. We then generalize the class of skew Young tableaux under consideration; this allows in particular to recover a formula for Eulerian numbers which is a direc...

Young’s lattice is a partial order on integer partitions whose saturated chains correspond to standard Young tableaux, one type of combinatorial object that generates the Schur basis for symmetric functions. Generalizing lattice, we introduce new weak compositions call key poset. Saturated in this poset objects generate polynomials, nonsymmetric polynomial generalization basis. skew functions, ...

We identify a subalgebra Ĥ + n of the extended affine Hecke algebra Ĥn of type A. The subalgebra Ĥ + n is a u-analogue of the monoid algebra of Sn n Z≥0 and inherits a canonical basis from that of Ĥn. We show that its left cells are naturally labeled by tableaux filled with positive integer entries having distinct residues mod n, which we term positive affine tableaux (PAT). We then exhibit a c...