2 papers
math.CO2024
Garsia--Remmel -rook numbers are not always unimodal
Joel Brewster Lewis, Alejandro H. Morales
We show by an explicit example that the Garsia--Remmel -rook numbers of Ferrers boards do not all have unimodal sequences of coefficients. This resolves in the negative a questi…
math.CO2024
LLT Polynomials and Hecke Algebra Traces
Alejandro H. Morales, Mark A. Skandera, Jiayuan Wang
We show that coefficients in unicellular LLT polynomials are evaluations of Hecke algebra traces at Kazhdan-Lusztig basis elements. We express these in terms of traditional trace b…