RELATION BETWEEN STATISTICS OF PERMUTATIONS
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Date
2013
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Journal ISSN
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Publisher
faculty of engineering and natural sciences
Abstract
Permutations have a remarkably rich combinatorial structure. Part of the reason for this is that a permutation of a finite set can be represented in many equivalent ways, including as a word (sequence), a function, a collection of disjoint cycles, a matrix, etc. Each of these representations suggests a host of natural invariants (or "statistics"), operations, transformations, structures, etc., that can be applied to or placed on permutations. The fundamental statistics, operations, and structures on permutations include descent set (with numerous specializations), excedance set, cycle type, records, subsequences, composition (product), partial orders, simplicial complexes, probability distributions, etc. This paper contains topics that relates to the main part and definitions to understand the main part of this work. In the main part, we consider statistics of permutations, equidistributions of them.
Description
Keywords
disjoint cycles, permutation, equidistribution
Citation
Fayziyev Sh / RELATION BETWEEN STATISTICS OF PERMUTATIONS / 6M060100-Science mathematics / 2013