• $n$-Color palindromic compositions with restricted subscripts

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/131/0009

• # Keywords

$n$-color compositions; generating functions; combinatorial identities.

• # Abstract

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.

• # Author Affiliations

1. Departamento de Matemáticas, Universidad del Cauca, Calle 5 No 4–70, Popayán, Colombia
2. Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia
3. Department of Mathematics, University of Tennessee, Knoxville, TN, USA

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019