Recent works in algebraic combinatorics have brought up to date the importance of certain planar structures, called ribbon tableaux, which are generalizations of Young tableaux. This paper gives an algorithm to eeciently distribute, using PVM, the computation of the set of all ribbon tableaux of given shape and weight. It also provides a way to compute the spin polynomials associated to those s...

We develop two combinatorial proofs of the fact that certain Young tableaux are counted by the Catalan numbers. The setting is a larger class of tableaux where labels increase along rows without attention to whether labels increase down columns. We define a new operation called tableau cycling. It is used to duplicate the reflection argument attributed to André in the tableaux setting, and also...

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...

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...