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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
A superdiagonal composition is one in which the $i$-th part or summand is of size greater than or equal to $i$. In this paper, we study the number of palindromic superdiagonal compositions and colored superdiagonal compositions. In particular, we giv
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
Jelinek, Mansour, and Shattuck studied Wilf-equivalence among pairs of patterns of the form ${sigma,tau}$ where $sigma$ is a set partition of size $3$ with at least two blocks. They obtained an upper bound for the number of Wilf-equivalence classes f
In this work, we give combinatorial proofs for generating functions of two problems, i.e., flushed partitions and concave compositions of even length. We also give combinatorial interpretation of one problem posed by Sylvester involving flushed parti
In this article we consider the cycle structure of compositions of pairs of involutions in the symmetric group S_n chosen uniformly at random. These can be modeled as modified 2-regular graphs, giving rise to exponential generating functions. A compo