TY - JOUR
T1 - The absolute order of a permutation representation of a Coxeter group
AU - Athanasiadis, Christos A.
AU - Roichman, Yuval
PY - 2014/2
Y1 - 2014/2
N2 - A permutation representation of a Coxeter group W naturally defines an absolute order. This family of partial orders (which includes the absolute order on W) is introduced and studied in this paper. Conditions under which the associated rank generating polynomial divides the rank generating polynomial of the absolute order on W are investigated when W is finite. Several examples, including a symmetric group action on perfect matchings, are discussed. As an application, a well-behaved absolute order on the alternating subgroup of W is defined.
AB - A permutation representation of a Coxeter group W naturally defines an absolute order. This family of partial orders (which includes the absolute order on W) is introduced and studied in this paper. Conditions under which the associated rank generating polynomial divides the rank generating polynomial of the absolute order on W are investigated when W is finite. Several examples, including a symmetric group action on perfect matchings, are discussed. As an application, a well-behaved absolute order on the alternating subgroup of W is defined.
KW - Absolute order
KW - Alternating subgroup
KW - Coxeter group
KW - Group action
KW - Modular element
KW - Perfect matching
KW - Rank generating polynomial
KW - Reflection arrangement
UR - http://www.scopus.com/inward/record.url?scp=84891630569&partnerID=8YFLogxK
U2 - 10.1007/s10801-013-0439-8
DO - 10.1007/s10801-013-0439-8
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AN - SCOPUS:84891630569
SN - 0925-9899
VL - 39
SP - 75
EP - 98
JO - Journal of Algebraic Combinatorics
JF - Journal of Algebraic Combinatorics
IS - 1
ER -