2 citations · 7 across the 18 of their papers we have counts for
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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…
Comodule Structures, Equivariant Hopf Structures, and Generalized Schubert Polynomials
Rui Xiong
In this article, the comodule structure of Chow rings of Flag manifolds is described by Schubert cells. Its equivariant version gives rise to a Hopf struct…
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…
Kernel-Cokernel Sequence for Composition and its Applications
Rui Xiong
If this article, an elementary kernel-cokernel exact sequence is introduced for . Some relative sequences and applications are dicussed. This r…
A short proof of Spectral Sequences of Filtered Complexes
Rui Xiong
The purpose of this article is to present my new proof of the the construction and the convergence theorem of spectral sequences of filtered complexes, which is much shorter and cl…
Direct proof of Mckay Correspondence and the representations of finite subgroups of
Rui Xiong
The classic Mckay correspondence gives a connection between finite subgroups of and the simply-laced Dynkin diagrams. In this article, a direct proof is pres…