New signed bijections pertaining to alternating sign matrices and Gelfand-Tsetlin patterns
APA
(2024). New signed bijections pertaining to alternating sign matrices and Gelfand-Tsetlin patterns. SciVideos. https://youtu.be/gHf0XdPHRyk
MLA
New signed bijections pertaining to alternating sign matrices and Gelfand-Tsetlin patterns. SciVideos, Oct. 23, 2024, https://youtu.be/gHf0XdPHRyk
BibTex
@misc{ scivideos_ICTS:30031,
doi = {},
url = {https://youtu.be/gHf0XdPHRyk},
author = {},
keywords = {},
language = {en},
title = {New signed bijections pertaining to alternating sign matrices and Gelfand-Tsetlin patterns},
publisher = {},
year = {2024},
month = {oct},
note = {ICTS:30031 see, \url{https://scivideos.org/icts-tifr/30031}}
}
Abstract
Alternating sign matrices (ASM) and descending plane partitions (DPP) both have the concept of rank, and it has been known that the same number of them exist for each rank (conjectured in 1983 by W. H. Mills, David P. Robbins and Howard Rumsey, Jr., and proved in 1996 by Doron Zeilberger and by Greg Kuperberg independently). However, no explicit bijections between them have been found so far. This problem is known as the ASM-DPP bijection problem.
In 2020, Fischer and Konvalinka constructed a bijection between ASM(n)xDPP(n-1) and ASM(n-1)xDPP(n), where ASM(n) denotes the set of ASMs with rank n, and it is similar for DPP(n). This bijection was developed using the concept of signed bijections. I introduce the notion of compatibility of signed bijections to measure the naturalness of signed bijections and to simplify the construction. In this talk, I present the definition of compatibility and some of the results obtained from it. For example, these include the refined structure of Ge...