TY - JOUR
T1 - Avoiding a pair of patterns in multisets and compositions
AU - Jelínek, Vít
AU - Mansour, Toufik
AU - Ramírez, José L.
AU - Shattuck, Mark
N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.
PY - 2022/2
Y1 - 2022/2
N2 - In this paper, we study the Wilf-type equivalence relations among multiset permutations. We identify all multiset equivalences among pairs of patterns consisting of a pattern of length three and another pattern of length at most four. To establish our results, we make use of a variety of techniques, including Ferrers-equivalence arguments, sorting by minimal/maximal letters, analysis of active sites and direct bijections. In several cases, our arguments may be extended to prove multiset equivalences for infinite families of pattern pairs. Our results apply equally well to the Wilf-type classification of compositions, and as a consequence, we obtain a complete description of the Wilf-equivalence classes for pairs of patterns of type (3,3) and (3,4) on compositions, with the possible exception of two classes of type (3,4).
AB - In this paper, we study the Wilf-type equivalence relations among multiset permutations. We identify all multiset equivalences among pairs of patterns consisting of a pattern of length three and another pattern of length at most four. To establish our results, we make use of a variety of techniques, including Ferrers-equivalence arguments, sorting by minimal/maximal letters, analysis of active sites and direct bijections. In several cases, our arguments may be extended to prove multiset equivalences for infinite families of pattern pairs. Our results apply equally well to the Wilf-type classification of compositions, and as a consequence, we obtain a complete description of the Wilf-equivalence classes for pairs of patterns of type (3,3) and (3,4) on compositions, with the possible exception of two classes of type (3,4).
KW - Composition
KW - Multiset
KW - Pattern avoidance
KW - Wilf-equivalence
UR - http://www.scopus.com/inward/record.url?scp=85118897223&partnerID=8YFLogxK
U2 - 10.1016/j.aam.2021.102286
DO - 10.1016/j.aam.2021.102286
M3 - Article
AN - SCOPUS:85118897223
SN - 0196-8858
VL - 133
SP - 102286
JO - Advances in Applied Mathematics
JF - Advances in Applied Mathematics
M1 - 102286
ER -