Anti-palindromic compositions

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.

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Work Title Anti-palindromic compositions
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Open Access
Creators
  1. George E Andrews
  2. Matthew Just
  3. Greg Simay
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. The Fibonacci Quarterly
Publication Date May 2022
Related URLs
Deposited August 17, 2022

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Version 1
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  • Created
  • Added Anti_Palindromic_Compositions__new___12_.pdf
  • Added Creator George E Andrews
  • Added Creator Matthew Just
  • Added Creator Greg Simay
  • Published
  • Updated Description Show Changes
    Description
    • A palindromic composition of n is a composition of n which can
    • be read the same way forwards and backwards. In this paper we de ne an
    • 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 de ning a new q-analogue of the Fibonacci sequence, which is related to
    • by de fining a new q-analogue of the Fibonacci sequence, which is related to
    • certain equivalence classes of anti-palindromic compositions.
  • Updated Description Show Changes
    Description
    • 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 de fining a new q-analogue of the Fibonacci sequence, which is related to
    • certain equivalence classes of anti-palindromic compositions.
    • 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 de fining a new _q_-analogue of the Fibonacci sequence, which is related to certain equivalence classes of anti-palindromic compositions.
  • Updated Description Show Changes
    Description
    • 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 de fining a new _q_-analogue of the Fibonacci sequence, which is related to certain equivalence classes of anti-palindromic compositions.
    • 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.
  • Updated Related URLs, Publication Date Show Changes
    Related URLs
    • https://www.fq.math.ca/60-2.html
    Publication Date
    • 2022-05-01
    • 2022-05
  • Updated