Equivalence classes of permutations modulo replacements between 123 and two-integer patterns
The electronic journal of combinatorics, Tome 21 (2014) no. 2
We explore a new type of replacement of patterns in permutations, suggested by James Propp, that does not preserve the length of permutations. In particular, we focus on replacements between 123 and a pattern of two integer elements. We apply these replacements in the classical sense; that is, the elements being replaced need not be adjacent in position or value. Given each replacement, the set of all permutations is partitioned into equivalence classes consisting of permutations reachable from one another through a series of bi-directional replacements. We break the eighteen replacements of interest into four categories by the structure of their classes and fully characterize all of their classes.
DOI :
10.37236/3753
Classification :
05A05, 05A18
Mots-clés : permutation patterns, pattern replacements
Mots-clés : permutation patterns, pattern replacements
Affiliations des auteurs :
Vahid Fazel-Rezai 1
@article{10_37236_3753,
author = {Vahid Fazel-Rezai},
title = {Equivalence classes of permutations modulo replacements between 123 and two-integer patterns},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {2},
doi = {10.37236/3753},
zbl = {1300.05009},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3753/}
}
Vahid Fazel-Rezai. Equivalence classes of permutations modulo replacements between 123 and two-integer patterns. The electronic journal of combinatorics, Tome 21 (2014) no. 2. doi: 10.37236/3753
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