Pattern avoidance is not P-recursive

Scott Garrabrant; Igor Pak

Pattern avoidance is not P-recursive

Combinatorics 2015-05-26 v1 Computational Complexity Formal Languages and Automata Theory

Authors: Scott Garrabrant , Igor Pak

Abstract

Let $F \subset S_k$ be a finite set of permutations and let $C_n(F)$ denote the number of permutations $\sigma$ in $S_n$ avoiding the set of patterns $F$ . The Noonan-Zeilberger conjecture states that the sequence ${C_n(F)}$ is P-recursive. We use Computability Theory to disprove this conjecture.

Keywords

pattern avoidance in permutations permutations integer sequences and recurrences

Cite

@article{arxiv.1505.06508,
  title  = {Pattern avoidance is not P-recursive},
  author = {Scott Garrabrant and Igor Pak},
  journal= {arXiv preprint arXiv:1505.06508},
  year   = {2015}
}

Comments

19 pages

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