• JOSE L RAMIREZ

      Articles written in Proceedings – Mathematical Sciences

    • $n$-Color palindromic compositions with restricted subscripts

      JHON J BRAVO JOSE L HERRERA JOSE L RAMIREZ MARK SHATTUCK

      More Details Abstract Fulltext PDF

      An $n$-color composition is one in which a part of size $m$ can come in $m$colors (denoted by subscripts). Compositions that read the same when read forwards or backwards are said to be palindromic. In this paper, we study the number of $n$ color palindromic compositions whose parts have subscripts belonging to a particular arithmetic progression. That is, the subscripts are of the form $\mathcal{l}a + b$, where $\mathcal{l}$ and $b$ are fixed positive integers and $a\geq 0$ is arbitrary. Among our results, we derive an explicit formula for the generating function and provide a connection with Riordan arrays. Finally, we describe bijections between certain restricted classes of palindromic $n$-color compositions and subsets of ordinary compositions and ternary words.

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