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      Permanent link:
      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

       

      JHON J BRAVO1 JOSE L HERRERA1 JOSE L RAMIREZ2 MARK SHATTUCK3

      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
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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