Xing Gao

collaborators

3 papers

math.CO2025

Weighted $K$ - $k$ -Schur functions and their application to the $K$ - $k$ -Schur alternating conjecture

Yaozhou Fan, Xing Gao

We introduce the new concept of weighted $K$ - $k$ -Schur functions -- a novel family within the broader class of Katalan functions -- that unifies and extends both $K$ - $k$ -Schur func…

math.CO2025

Lowering operators on $K$ - $k$ -Schur functions and a lowering operator formula for closed $K$ - $k$ -Schur functions

Yaozhou Fang, Xing Gao, Li Guo

This paper gives a systematic study of the lowering operators acting on the $K$ - $k$ -Schur functions, motivated by the pivotal role played by the operators in the definition and stu…

math.CO2025

Alternating dual Pieri rule conjecture and $k$ -branching conjecture of closed $k$ -Schur Katalan functions

Yaozhou Fang, Xing Gao

For closed $k$ -Schur Katalan functions $\fgÎ»{k}$ with $k$ a positive integer and $I^»$ a $k$ -bounded partition, Blasiak, Morse and Seelinger proposed the alternating dual Pieri rul…

Weighted K-k-Schur functions and their application to the K-k-Schur alternating conjecture

Lowering operators on K-k-Schur functions and a lowering operator formula for closed K-k-Schur functions

Alternating dual Pieri rule conjecture and k-branching conjecture of closed k-Schur Katalan functions

Weighted $K$ - $k$ -Schur functions and their application to the $K$ - $k$ -Schur alternating conjecture

Lowering operators on $K$ - $k$ -Schur functions and a lowering operator formula for closed $K$ - $k$ -Schur functions

Alternating dual Pieri rule conjecture and $k$ -branching conjecture of closed $k$ -Schur Katalan functions