Timeline for Plane partitions as sums of determinants

12 events

when toggle format	what		by	license	comment
May 13, 2023 at 21:10	vote	accept	T. Amdeberhan
May 1, 2023 at 5:22	answer	added	Fedor Petrov		timeline score: 4
Apr 30, 2023 at 15:55	answer	added	Richard Stanley		timeline score: 7
Apr 30, 2023 at 14:14	history	edited	T. Amdeberhan	CC BY-SA 4.0	added 29 characters in body
Apr 30, 2023 at 13:52	history	edited	T. Amdeberhan	CC BY-SA 4.0	added 398 characters in body
Apr 30, 2023 at 11:45	comment	added	Fedor Petrov		Hm, looks like Binet-Cauchy. This $V(\mathbf{J})/V(\mathbf{J})$ is a determinant of an $m\times m$ matrix $(f_{k-1}(j_i))_{k, i\in [m]}$, where $f_k(x)$ is a polynomial of degree $k$ with leading coefficient $1/k!$, for example $f_k(x)={x+c_k\choose k} $ for some $c_k$. If I am not mistaken, this gives a determinant ${i+j+m+n\choose m+n-1}_{0\le i, j\le m-1}$. That has some LGV interpretation but not which immediately gives these 3d Young diagrams in a box.
Apr 29, 2023 at 21:29	history	edited	T. Amdeberhan	CC BY-SA 4.0	added 122 characters in body
Apr 29, 2023 at 21:24	history	edited	T. Amdeberhan	CC BY-SA 4.0	added 122 characters in body
Apr 29, 2023 at 20:54	history	edited	T. Amdeberhan	CC BY-SA 4.0	added 180 characters in body
Apr 29, 2023 at 15:27	history	edited	T. Amdeberhan	CC BY-SA 4.0	deleted 8 characters in body
Apr 28, 2023 at 23:30	comment	added	darij grinberg		Related (also unanswered!): math.stackexchange.com/questions/3367836/…
Apr 28, 2023 at 21:49	history	asked	T. Amdeberhan	CC BY-SA 4.0