arXiv subjects
Publications and source records attributed to Yaozhou Fang.
Motivated by the Morse--Seelinger conjecture on type C $k$-Schur functions, we develop a permutation model for type C strong marked tableaux. Using type C transpositions, we give an explicit correspondence with the symmetric-core model that preserves the marking data. We also describe the induced affine Weyl group action on bounded partitions.
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 study of Katalan functions. A lowering operator formula for closed $K$-$k$-Schur functions is obtained. As an application, a combinatorial proof is provided to a conjecture on closed $k$-Schur Katalan functions, posed by Blasiak, Morse and Seelinger, and recently proved by Ikeda, Iwao and Naito by a different method.
For closed $k$-Schur Katalan functions $\fgλ{k}$ with $k$ a positive integer and $λ$ a $k$-bounded partition, Blasiak, Morse and Seelinger proposed the alternating dual Pieri rule conjecture and the $k$-branching conjecture. In the present paper, we positively prove the first one for large enough $k$ and for strictly decreasing partitions $λ$ respectively, as well as the second one for strictly decreasing partitions $λ$.