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Real-rootedness of the type A minuscule polynomials
- Publication Year :
- 2023
-
Abstract
- We prove two recent conjectures of Bourn and Erickson (2023) regarding the real-rootedness of a certain family of polynomials $N_n(t)$ as well as the sum of their coefficients. These polynomials arise as the numerators of generating functions in the context of the discrete one-dimensional earth mover's distance (EMD) and have also connection to the Wiener index of minuscule lattices. We also prove that the coefficients of $N_n(x)$ are asymptotically normal, the coefficient matrix of $N_n(x)$ is totally positive and the polynomial sequence $N_n(x)$'s is $x$-log-concave.<br />Comment: 13 pages, some typos are corrected
- Subjects :
- Mathematics - Combinatorics
05A15, 05A10, 15B36, 62E20, 05A19
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2308.16782
- Document Type :
- Working Paper