Weighted K-k-Schur functions interpolate between two known Katalan function families, and their recursive expansion proves the K-k-Schur alternating conjecture for partitions whose first b_lambda parts are strictly decreasing.
Lowering operators on $K$-$k$-Schur functions and a lowering operator formula for closed $K$-$k$-Schur functions
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
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.
citation-role summary
background 1
citation-polarity summary
fields
math.CO 1years
2025 1verdicts
ACCEPT 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Weighted $K$-$k$-Schur functions and their application to the $K$-$k$-Schur alternating conjecture
Weighted K-k-Schur functions interpolate between two known Katalan function families, and their recursive expansion proves the K-k-Schur alternating conjecture for partitions whose first b_lambda parts are strictly decreasing.