# A relation on 132-avoiding permutation patterns

Abstract : A permutation $σ$ contains the permutation $τ$ if there is a subsequence of $σ$ order isomorphic to $τ$. A permutation $σ$ is $τ$-avoiding if it does not contain the permutation $τ$. For any $n$, the popularity of a permutation $τ$, denoted $A$n(τ), is the number of copies of τ contained in the set of all 132-avoiding permutations of length n. Rudolph conjectures that for permutations τ and μ of the same length, A$n$($τ$) ≤ $A$n(μ) for all n if and only if the spine structure of τ is less than or equal to the spine structure of μ in refinement order. We prove one direction of this conjecture, by showing that if the spine structure of τ is less than or equal to the spine structure of μ, then A$n$($τ$) ≤ $A$$n$($μ$) for all $n$. We disprove the opposite direction by giving a counterexample, and hence disprove the conjecture.
Keywords :
Document type :
Journal articles

Cited literature [6 references]

https://hal.inria.fr/hal-01349056
Contributor : Coordination Episciences Iam <>
Submitted on : Tuesday, July 26, 2016 - 5:57:33 PM
Last modification on : Wednesday, February 19, 2020 - 1:10:04 PM

### File

2375-9839-1-PB.pdf
Explicit agreement for this submission

### Identifiers

• HAL Id : hal-01349056, version 1

### Citation

Natalie Aisbett. A relation on 132-avoiding permutation patterns. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no.2 (2), pp.285-302. ⟨hal-01349056⟩

Record views