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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

Inverse-Conjugate Compositions Modulo \(m\)

Augustine O. Munagi1
1John Knopfmacher Center for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, P.o. Wrrs, 2050 Johannesburg, South Africa
  • Published: 30/09/2019

Abstract

We consider inverse-conjugate compositions of a positive integer \(n\) in which the parts belong to the residue class of 1 modulo an integer \(m > 0\). It is proved that such compositions exist only for values of \(n\) that belong to the residue class of 1 modulo 2m. An enumerations results is provided using the properties of inverse-conjugate compositions. This work extends recent results for inverse-conjugate compositions with odd parts.

Keywords: composition, inverse-conjugate, residue class, combinatorial identity
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Citation
Augustine O. Munagi. Inverse-Conjugate Compositions Modulo \(m\)[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 110. -. DOI: .