# Equidistribution of descents, adjacent pairs, and place-value pairs on permutations

Deutsch, Emeric and Kitaev, Sergey and Remmel, Jeffrey
(2009)
*Equidistribution of descents, adjacent pairs, and place-value pairs on permutations.*
Journal of Integer Sequences, 12 (5).

## Abstract

An $(X,Y)$-descent in a permutation is a pair of adjacent elements such that the first element is from $X$, the second element is from $Y$, and the first element is greater than the second one. An $(X,Y)$-adjacency in a permutation is a pair of adjacent elements such that the first one is from $X$ and the second one is from $Y$. An $(X,Y)$-place-value pair in a permutation is an element $y$ in position $x$, such that $y$ is in $Y$ and $x$ is in $X$. It turns out, that for certain choices of $X$ and $Y$ some of the three statistics above become equidistributed. Moreover, it is easy to derive the distribution formula for $(X,Y)$-place-value pairs thus providing distribution for other statistics under consideration too. This generalizes some results in the literature. As a result of our considerations, we get combinatorial proofs of several remarkable identities. We also conjecture existence of a bijection between two objects in question preserving a certain statistic.

Item type: | Article |
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ID code: | 49893 |

Keywords: | adjacent pairs, permutations, bijection, Mathematics, Discrete Mathematics and Combinatorics |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Computer and Information Sciences |

Depositing user: | Pure Administrator |

Date deposited: | 17 Oct 2014 14:49 |

Last modified: | 07 Jan 2017 04:21 |

URI: | https://strathprints.strath.ac.uk/id/eprint/49893 |

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