|
This article is cited in 2 scientific papers (total in 2 papers)
One-dimensional central measures on numberings of ordered sets
A. M. Vershikabc a Saint Petersburg State University
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
Abstract:
We describe one-dimensional central measures on numberings (tableaux) of ideals
of partially ordered sets (posets). As the main example, we study the poset $\mathbb{Z}_+^d$ and the graph
of its finite ideals, multidimensional Young tableaux; for $d=2$, this is the ordinary
Young graph. The central measures are stratified by dimension; in the paper we give a complete description
of the one-dimensional stratum and prove that every ergodic central measure is uniquely determined
by its frequencies. The suggested method, in particular, gives the first purely combinatorial
proof of E. Thoma's theorem for one-dimensional central measures different from the Plancherel measure
(which is of dimension $2$).
Keywords:
posets, ideals, numberings, central measures.
Received: 27.09.2022 Revised: 27.09.2022 Accepted: 01.10.2022
Citation:
A. M. Vershik, “One-dimensional central measures on numberings of ordered sets”, Funktsional. Anal. i Prilozhen., 56:4 (2022), 17–24; Funct. Anal. Appl., 56:4 (2022), 251–256
Linking options:
https://www.mathnet.ru/eng/faa4048https://doi.org/10.4213/faa4048 https://www.mathnet.ru/eng/faa/v56/i4/p17
|
Statistics & downloads: |
Abstract page: | 167 | Full-text PDF : | 8 | References: | 43 | First page: | 15 |
|