arXiv subjects

Shogo Sugimoto

Publications and source records attributed to Shogo Sugimoto.

2 recordsLinked to original sources

arXiv2026

Symmetry of the generating function of semistandard oscillating tableaux

H.Choi-D.Kim-S.J.Lee and S.J.Lee introduced a new kind of tableaux, semistandard oscillating tableaux (SSOT), around 2024 in the context of Lusztig $q$-weight multiplicities, KR crystals and King tableaux. In this paper, we study generating function of the SSOTs and its symmetry. First, we extend Gessel's and Assaf-Searles' expansion of a Schur function in terms of fundamental quasi-symmetric functions to our generating function. As a consequence, we show that it is $F$-positive. Further, we improve Sundaram's work on oscillating tableaux by proving that it is symmetric, Schur-positive, and has Saturated Newton polytope.

math.CO↗

arXiv2019

Factorial Flagged Grothendieck Polynomials

We show that the factorial flagged Grothendieck polynomials defined by flagged set-valued tableaux of Knutson-Miller-Yong can be expressed by a Jacobi-Trudi type determinant formula, generalizing the work of Hudson-Matsumura. In particular, we obtain an alternative proof of the tableau and determinant formulas of vexillary double Grothendieck polynomials, that have been obtained by Knutson-Miller-Yong and Hudson-Matsumura respectively. Moreover, we show that each factorial flagged Grothendieck polynomial can be obtained from a product of linear polynomials by applying K-theoretic divided difference operators.

math.CO↗