Enumerating Permutations by their Run Structure

Christopher. J. Fewster; Daniel Siemssen

Enumerating Permutations by their Run Structure

Christopher. J. Fewster, Daniel Siemssen

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Motivated by a problem in quantum field theory, we study the up and down structure of circular and linear permutations. In particular, we count the length of the (alternating) runs of permutations by representing them as monomials and find that they can always be decomposed into so-called `atomic' permutations introduced in this work. This decomposition allows us to enumerate the (circular) permutations of a subset of the natural numbers by the length of their runs. Furthermore, we rederive, in an elementary way and using the methods developed here, a result due to Kitaev on the enumeration of valleys.

Original language	English
Article number	P4.18
Number of pages	19
Journal	ELECTRONIC JOURNAL OF COMBINATORICS
Volume	21
Issue number	4
Publication status	Published - 23 Oct 2014

Bibliographical note

19 pages

Keywords

Enumerative combinatorics
permutations

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Cite this

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N2 - Motivated by a problem in quantum field theory, we study the up and down structure of circular and linear permutations. In particular, we count the length of the (alternating) runs of permutations by representing them as monomials and find that they can always be decomposed into so-called `atomic' permutations introduced in this work. This decomposition allows us to enumerate the (circular) permutations of a subset of the natural numbers by the length of their runs. Furthermore, we rederive, in an elementary way and using the methods developed here, a result due to Kitaev on the enumeration of valleys.

AB - Motivated by a problem in quantum field theory, we study the up and down structure of circular and linear permutations. In particular, we count the length of the (alternating) runs of permutations by representing them as monomials and find that they can always be decomposed into so-called `atomic' permutations introduced in this work. This decomposition allows us to enumerate the (circular) permutations of a subset of the natural numbers by the length of their runs. Furthermore, we rederive, in an elementary way and using the methods developed here, a result due to Kitaev on the enumeration of valleys.

KW - Enumerative combinatorics

KW - permutations

M3 - Article

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JO - ELECTRONIC JOURNAL OF COMBINATORICS

JF - ELECTRONIC JOURNAL OF COMBINATORICS

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