A Spectral Approach to Consecutive Pattern-Avoiding Permutations

Details A Spectral Approach to Consecutive Pattern-Avoiding Permutations A Spectral Approach to Consecutive Pattern-Avoiding Permutations

2010-09-10

arxiv.org/abs/1009.2119v2

Mathematics

Combinatorics

a reference is added; corrected typos; to appear in Journal of Combinatorics

Scientific paper

We consider the problem of enumerating permutations in the symmetric group on $n$ elements which avoid a given set of consecutive pattern $S$, and in particular computing asymptotics as $n$ tends to infinity. We develop a general method which solves this enumeration problem using the spectral theory of integral operators on $L^{2}([0,1]^{m})$, where the patterns in $S$ has length $m+1$. Kre\u{\i}n and Rutman's generalization of the Perron--Frobenius theory of non-negative matrices plays a central role. Our methods give detailed asymptotic expansions and allow for explicit computation of leading terms in many cases. As a corollary to our results, we settle a conjecture of Warlimont on asymptotics for the number of permutations avoiding a consecutive pattern.

Affiliated with

Also associated with

No associations

Rating

A Spectral Approach to Consecutive Pattern-Avoiding Permutations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Spectral Approach to Consecutive Pattern-Avoiding Permutations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Spectral Approach to Consecutive Pattern-Avoiding Permutations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-562380