Abstract In 2010, Rhoades proved that promotion on rectangular standard Young tableaux, together with the associated fake-degree polynomial, provides an instance of cyclic sieving phenomenon. We extend this result to m -tuples skew tableaux same shape, for fixed , subject condition th power polynomial evaluates nonnegative integers at roots unity. However, we are unable specify explicit group a...

The Wronski map is a finite, PGL2(C)-equivariant morphism from the Grassmannian Gr(d, n) to a projective space (the projectivization of a vector space of polynomials). We consider the following problem. If Cr ⊂ PGL2(C) is a cyclic subgroup of order r, how may Cr-fixed points are in the fibre of the Wronski map over a Cr-fixed point in the base? In this paper, we compute a general answer in term...

In 1977 G.P. Thomas has shown that the sequence of Schur polynomials associated to a partition can be comfortabely generated from the sequence of variables x = (x1; x2; x3; : : :) by the application of a mixed shift/multiplication operator, which in turn can be easily computed from the set SY T () of standard Young tableaux of shape. We generalise this construction, thereby making possible | fo...

Young tableaux are ubiquitous combinatorial objects making important and inspiring appearances in representation theory, geometry and algebra. They naturally arise in the study of symmetric functions, representation theory of the symmetric and complex general linear groups, and Schubert calculus of Grassmannians. Discovering and interpreting enumerative formulas for Young tableaux (and their ge...

We prove an inequality for the Kostka Foulkes polynomials Kλ,μ(q). As a corollary, we obtain a nontrivial lower bound for the Kostka numbers and a new proof of the Berenstein Zelevinsky weight-multiplicity-one-criterium. The concept of Young tableau plays an important role in the representation theory of the symmetric and general linear groups. Based on the pioneering fundamental works of G. Fr...

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 quasisy...

We present a randomized algorithm for generating standard set-valued tableaux by extending the Green-Nijenhuis-Wilf hook walk algorithm. In case of asymptotically rank two partitions, we use this to give fully polynomial almost uniform sampler (FPAUS) tableaux. This FPAUS is then used construct approximation scheme (FPRAS) counting number such shapes. also and FPRAS when either size partition o...

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...