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Principal specializations of Grothendieck polynomials
Haojun Bai, Feng Gu, Peter L. Guo +1
Motivated by Stanley's ``Schubert shenanigans'' paper, commendable attempts have been made to understand the principal specializations of Schubert or Grothendieck polynomials. In t…
A Pieri type formula for motivic Chern classes of Schubert cells in Grassmannians
Neil J. Y. Fan, Peter L. Guo, Changjian Su +1
We prove a Pieri formula for motivic Chern classes of Schubert cells in the equivariant K-theory of Grassmannians, which is described in terms of ribbon operators on partitions. Ou…
Bumpless pipe dreams meet Puzzles
Neil J. Y. Fan, Peter L. Guo, Rui Xiong
Knutson and Zinn-Justin recently found a puzzle rule for the expansion of the product of two double Grothendieck polynomials inde…
Pieri and Murnaghan--Nakayama type Rules for Chern classes of Schubert Cells
Neil J. Y. Fan, Peter L. Guo, Rui Xiong
We develop Pieri type as well as Murnaghan--Nakayama type formulas for equivariant Chern--Schwartz--MacPherson classes of Schubert cells in the classical flag variety. These formul…
Poincaré Polynomials of Odd Diagram Classes
Neil J. Y. Fan, Peter L. Guo
An odd diagram class is a set of permutations with the same odd diagram. Brenti, Carnevale and Tenner showed that each odd diagram class is an interval in the Bruhat order. They co…
An Involution on Semistandard Skyline Fillings
Neil J. Y. Fan, Peter L. Guo, Nicolas Y. Liu
Non-attacking skyline fillings were used by Haglund, Haiman and Loehr to establish a combinatorial formula for nonsymmetric Macdonald polynomials. Semistandard skyline fillings are…