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Register a new userCompositions that are palindromic modulo $m$
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Authors
Matthew Just
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In recent work, G. E. Andrews and G. Simay prove a surprising relation involving parity palindromic compositions, and ask whether a combinatorial proof can be found. We extend their results to a more general class of compositions that are palindromic modulo $m$, that includes the parity palindromic case when $m=2$. We then provide combinatorial proofs for the cases $m=2$ and $m=3$.
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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
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