6 papers · 1 filter
Generalized staircase partitions and Macdonald principal specializations
Tatsushi Shimazaki
Generalized staircase partitions are obtained by replacing each box of an ordinary staircase with a fixed rectangle. Between consecutive generalized staircases, we determine the un…
Crystals and sign-reversing involutions for set-valued skew tableaux and decorated states of the five-vertex model
Tatsushi Shimazaki
We construct bijections among semistandard set-valued tableaux of skew shape, marked Gelfand-Tsetlin patterns, and decorated states of the five-vertex model with boundary data dete…
Staircase hook-length ratios and special values of Jacobi polynomials
Tatsushi Shimazaki
We relate hook-length products for adjacent staircase partitions to special values of Jacobi polynomials. This connection expresses the number of semistandard tableaux in terms of…
Special values of -theoretic Schur - and -functions
Takahiko Nobukawa, Tatsushi Shimazaki
We provide the special values of the skew version of the -theoretic Schur - and -functions. Using these special values, we show an oddness property of the number of shifte…
Special values of Grothendieck polynomials in terms of hypergeometric functions
Taikei Fujii, Takahiko Nobukawa, Tatsushi Shimazaki
We give some special values of Grothendieck polynomials and an explicit formula for the number of set-valued tableaux. For Young diagrams consisting of a single row or a single col…
A recursive method for the oddness of the number of set-valued tableaux
Taikei Fujii, Takahiko Nobukawa, Tatsushi Shimazaki
Set-valued tableaux, introduced by Buch to express the tableaux-sum formula for stable Grothendieck polynomials, generalize semistandard tableaux. We provide a new recursive proof…