Statistics on restricted Fibonacci words

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Egecloglu Omer

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Journal Paper

Paper Information

Journal: TRANSACTIONS ON COMBINATORICS Year:2021 | Volume:10 | Issue:1 Page(s): 31-42

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Information Journal Paper

Title

Statistics on restricted Fibonacci words

Author(s)

Egecloglu Omer | Issue Writer Certificate

Keywords

Major index

inversion

Fibonacci

Abstract

We study two foremost Mahonian statistics, the Major index and the inversion number for a class of binary words called restricted Fibonacci words. The language of restricted Fibonacci words satisfies recurrences which allow for the calculation of the generating functions in two different ways. These yield identities involving the $q$-binomial coefficients and provide non-standard $q$-analogues of the Fibonacci numbers. The Major index generating function for restricted Fibonacci words turns out to be a $q$-power multiple of the inversion generating function.

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