A palindromic composition of n is a composition of n which can be read the same way forwards and backwards. In this paper we define an anti-palindromic composition of n to be a composition of n which has no mirror symmetry amongst its parts. We then give a surprising connection between the number of anti-palindromic compositions of n and the so-called tribonacci sequence, a generalization of the Fibonacci sequence. We conclude by defining a new q-analogue of the Fibonacci sequence, which is related to certain equivalence classes of anti-palindromic compositions.
This article appeared in the Fibonacci Quarterly.
|Work Title||Anti-palindromic compositions|
|License||In Copyright (Rights Reserved)|
|Publication Date||May 2022|
|Deposited||August 17, 2022|
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