02-26

On the diagram of 132-avoiding permutations

by Reifegerste, A.

 

Preprint series: 02-26, Preprints

MSC:
05A05 Combinatorial choice problems (subsets, representatives, permutations)
05A15 Exact enumeration problems, generating functions, See Also {33Cxx, 33Dxx}

 

Abstract: The diagram of a 132-avoiding permutation can easily be characterized: it is simply the diagram of a partition. Based on this fact, we present a new bijection between 132-avoiding and 321-avoiding permutations. We will show that this bijection translates the correspondences between these permutations and Dyck paths given by Krattenthaler and by Billey-Jockusch-Stanley, respectively, to each other. Moreover, the diagram approach yields simple proofs for some enumerative results concerning forbidden patterns in 132-avoiding permutations.

Keywords: 132-avoiding permutation, 321-avoiding permutation, diagram of a permutation, partition, Young diagram, Dyck path, permutation pattern


The author(s) agree, that this abstract may be stored asfull text and distributed as such by abstracting services.

Letzte Änderung: 01.03.2018 - Ansprechpartner: Webmaster