The number of {1243, 2134}-avoiding permutations
David Callan
TL;DR
This paper establishes that the counting sequence for permutations avoiding the patterns 1243 and 2134 has an algebraic generating function, linking it to a known sequence in the OEIS.
Contribution
It identifies the algebraic generating function for permutations avoiding specific patterns, connecting it to a known integer sequence.
Findings
The sequence is algebraic and matches OEIS sequence A164651.
Permutations avoiding 1243 and 2134 are characterized by this algebraic generating function.
The result provides a new link between pattern avoidance and algebraic generating functions.
Abstract
We show that the counting sequence for permutations avoiding both of the (classical) patterns 1243 and 2134 has the algebraic generating function supplied by Vaclav Kotesovec for sequence A164651 in The On-Line Encyclopedia of Integer Sequences.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Coding theory and cryptography · semigroups and automata theory