Weak Generalized Lifting Property, Bruhat Intervals, and Coxeter Matroids

被引：5

作者：

Caselli, Fabrizio ^{[1
]}

D'Adderio, Michele ^{[2
]}

Marietti, Mario ^{[3
]}

机构：

[1] Univ Bologna, Dipartimento Matemat, Piazza Porta San Donato 5, I-40126 Bologna, Italy

[2] Univ Libre Bruxelles ULB, Dept Math, Blvd Triomphe, B-1050 Brussels, Belgium

[3] Univ Politecn Marche, Dipartimento Ingn Ind & Sci Matemat, Via Brecce Bianche, I-60131 Ancona, Italy

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2021年 / 2021卷 / 03期

关键词：

D O I：

10.1093/imrn/rnaa124

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide a weaker version of the generalized lifting property that holds in complete generality for all Coxeter groups, and we use it to show that every parabolic Bruhat interval of a finite Coxeter group is a Coxeter matroid. We also describe some combinatorial properties of the associated polytopes.

引用

页码：1678 / 1698

页数：21

共 24 条

[1] The generalized lifting property of Bruhat intervals
Caselli, Fabrizio
Sentinelli, Paolo
JOURNAL OF ALGEBRAIC COMBINATORICS, 2017, 45 (03) : 687 - 700
[2] The generalized lifting property of Bruhat intervals
Fabrizio Caselli
Paolo Sentinelli
Journal of Algebraic Combinatorics, 2017, 45 : 687 - 700
[3] BRUHAT INTERVALS AND PARABOLIC COSETS IN ARBITRARY COXETER GROUPS
Marietti, Mario
arXiv, 2022,
[4] Bruhat intervals and parabolic cosets in arbitrary Coxeter groups
Marietti, Mario
JOURNAL OF ALGEBRA, 2023, 614 : 1 - 4
[5] Bruhat intervals, subword complexes and brick polyhedra for finite Coxeter groups
Dennis Jahn
Christian Stump
Mathematische Zeitschrift, 2023, 304
[6] Bruhat intervals, subword complexes and brick polyhedra for finite Coxeter groups
Jahn, Dennis
Stump, Christian
MATHEMATISCHE ZEITSCHRIFT, 2023, 304 (02)
[7] A FINITE COXETER GROUP THE WEAK BRUHAT ORDER OF WHICH IS NOT SYMMETRICAL CHAIN
LECLERC, B
EUROPEAN JOURNAL OF COMBINATORICS, 1994, 15 (02) : 181 - 185
[8] ON GENERALIZED WEAK I-LIFTING MODULES
Amouzegar, Tayyebeh
ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2016, (36): : 65 - 72
[9] On generalized weak i-lifting modules
Amouzegar, Tayyebeh (t.amouzgar@qiet.ac.ir), 2016, Forum-Editrice Universitaria Udinese SRL (36):
[10] Generalized nil-Coxeter algebras, cocommutative algebras, and the PBW property
Khare, Apoorva
GROUPS, RINGS, GROUP RINGS, AND HOPF ALGEBRAS, 2017, 688 : 139 - 168

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