Browsing by Author "Fayziyev Sh."

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    RELATION BETWEEN STATISTICS OF PERMUTATIONS
    (faculty of engineering and natural sciences, 2013) Fayziyev Sh.
    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.