Bender-Knuth involutions on linear extensions of posets

被引：0

作者：

Chiang, Judy Hsin-Hui ^{[1
]}

Hoang, Anh Trong Nam ^{[2
]}

Kendall, Matthew ^{[3
]}

Lynch, Ryan ^{[4
]}

Nguyen, Son ^{[2
]}

Przybocki, Benjamin ^{[5
]}

Xia, Janabel ^{[6
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL USA

[2] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

[3] Princeton Univ, Dept Math, Princeton, NJ USA

[4] Univ Notre Dame, Dept Math, Notre Dame, IN USA

[5] Stanford Univ, Dept Math, Stanford, CA USA

[6] MIT, Dept Math, Cambridge, MA USA

来源：

DISCRETE MATHEMATICS | 2024年 / 347卷 / 09期

关键词：

Bender-Knuth involution; Berenstein-Kirillov group; Linear extension; Cactus group; CONJECTURE;

D O I：

10.1016/j.disc.2024.114068

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the permutation group BKP generated by Bender-Knuth moves on linear extensions of a poset P , an analog of the Berenstein-Kirillov group on column-strict tableaux. We explore the group relations, with an emphasis on identifying posets P for which the cactus relations hold in BKP. We also examine BKP as a subgroup of the symmetric group S L( P ) on the set of linear extensions of P with the focus on analyzing posets P for which BKP = S L( P ) . (c) 2024 Elsevier B.V. All rights reserved.

引用

页数：20

共 50 条

[1] Bender-Knuth involutions for types B and C
Gutierrez, Alvaro
ELECTRONIC JOURNAL OF COMBINATORICS, 2024, 31 (02):
[2] Refined dual stable Grothendieck polynomials and generalized Bender-Knuth involutions
Galashin, Pavel
Grinberg, Darij
Liu, Gaku
ELECTRONIC JOURNAL OF COMBINATORICS, 2016, 23 (03):
[3] A PROOF OF THE BENDER-KNUTH CONJECTURE
GORDON, B
PACIFIC JOURNAL OF MATHEMATICS, 1983, 108 (01) : 99 - 113
[4] Bender-Knuth Billiards in Coxeter Groups
Barkley, Grant
Defant, Colin
Hodges, Eliot
Kravitz, Noah
Lee, Mitchell
FORUM OF MATHEMATICS SIGMA, 2025, 13
[5] Another refinement of the Bender-Knuth (ex-)conjecture
Fischer, I
EUROPEAN JOURNAL OF COMBINATORICS, 2006, 27 (02) : 290 - 321
[6] PLANE PARTITIONS .2. EQUIVALENCE OF BENDER-KNUTH AND MACMAHON CONJECTURES
ANDREWS, GE
PACIFIC JOURNAL OF MATHEMATICS, 1977, 72 (02) : 283 - 291
[7] LINEAR EXTENSIONS OF DIAMOND POSETS
Ju, Hyeong-Kwan
Seo, Seunghyun
HONAM MATHEMATICAL JOURNAL, 2019, 41 (04): : 863 - 870
[8] LINEAR EXTENSIONS OF INFINITE POSETS
BRIGHTWELL, GR
DISCRETE MATHEMATICS, 1988, 70 (02) : 113 - 136
[9] PERMUTATION STATISTICS AND LINEAR EXTENSIONS OF POSETS
BJORNER, A
WACHS, ML
JOURNAL OF COMBINATORIAL THEORY SERIES A, 1991, 58 (01) : 85 - 114
[10] GENERATING LINEAR EXTENSIONS OF POSETS BY TRANSPOSITIONS
RUSKEY, F
JOURNAL OF COMBINATORIAL THEORY SERIES B, 1992, 54 (01) : 77 - 101

← 1 2 3 4 5 →