Robinson–Schensted correspondence for unit interval orders

Autor:	Dongkwan Kim, Pavlo Pylyavskyy
Rok vydání:	2021
Předmět:	Symmetric function Combinatorics Mathematics::Combinatorics Conjecture Symmetric group General Mathematics General Physics and Astronomy Order (ring theory) Robinson–Schensted correspondence Equivalence (measure theory) Equivalence class Unit interval Mathematics
Zdroj:	Selecta Mathematica. 27
ISSN:	1420-9020 1022-1824
Popis:	The Stanley–Stembridge conjecture associates a symmetric function to each natural unit interval order $$\mathcal {P}$$ . In this paper, we define relations a la Knuth on the symmetric group for each $$\mathcal {P}$$ and conjecture that the associated $$\mathcal {P}$$ -Knuth equivalence classes are Schur-positive, refining theorems of Gasharov, Brosnan-Chow, Guay-Paquet, and Shareshian-Wachs. The resulting equivalence graphs fit into the framework of D graphs studied by Assaf. Furthermore, we conjecture that the Schur expansion is given by column-readings of $$\mathcal {P}$$ -tableaux that occur in the equivalence class. We prove these conjectures for $$\mathcal {P}$$ avoiding two specific suborders by introducing $$\mathcal {P}$$ -analog of Robinson–Schensted insertion, giving an answer to a long standing question of Chow.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c3f9fc599bb9224023d5a676e5aba630 https://doi.org/10.1007/s00029-021-00708-4 Zobrazit plný text záznamu Full text from SpringerLink