2 citations · 7 across the 18 of their papers we have counts for
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Combinatorial Aspects of Elliptic Schubert Calculus
Cristian Lenart, Rui Xiong, Changlong Zhong
The main goal of this paper is to extend two fundamental combinatorial results in Schubert calculus on flag manifolds from equivariant cohomology and -theory to equivariant elli…
Hybrid Pipe Dreams for Key Polynomials
Yihan Xiao, Rui Xiong, Haofeng Zhang
We develop a family of new combinatorial models for key polynomials. It is similar to the hybrid pipe dream model for Schubert polynomials defined recently by Knutson and Udell.
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…
Cauchy Formulas and Billey's Formulas for Generalized Grothendieck polynomials
Rui Xiong
We study the generalized double -Grothendieck polynomials for all types. We study the Cauchy formulas for them. Using this, we deduce the K-theoretic version of the comodule str…
Puzzle Model for Bumpless Pipe Dream
Rui Xiong
In this note, a new puzzle is introduced where the pipe dream and bumpless pipe dream can be played simultaneously. Using these, a combinatorial proof of the (ordinary) Schubert po…
A bijection proof of the Capelli's identity
Rui Xiong
In this article, a short combinatorial proof of the Capelli's identity is given. It also leads to an easy proof of the Capelli--Cauchy--Binet identity, a more general form of Capel…
Schur Polynomials through Lindström Gessel Viennot Lemma
Rui Xiong
In this article, we use Lindström Gessel Viennot Lemma to give a short, combinatorial, visualizable proof of the identity of Schur polynomials -- the sum of monomials of Young tabl…