Journal of Combinatorics

Volume 12 (2021)

Number 2

Restricted color $n$-color compositions

Pages: 355 – 377

DOI: https://dx.doi.org/10.4310/JOC.2021.v12.n2.a8

Authors

Brian Hopkins (Saint Peter’s University, Jersey City, New Jersey, U.S.A.)

Hua Wang (Georgia Southern University, Statesboro, Ga., U.S.A.)

Abstract

Agarwal introduced $n$-color compositions in 2000 and most subsequent research has focused on restricting which parts are allowed. Here we focus instead on restricting allowed colors. After three general results, giving recurrence formulas for the cases of given allowed colors, given prohibited colors, and colors satisfying modular conditions, we consider several more specific conditions, establishing direct formulas and connections to other combinatorial objects. Proofs are combinatorial, mostly using the notion of spotted tilings introduced by the first named author in 2012.

Keywords

compositions, $n$-color compositions, recurrence relations, exact enumeration, bijective combinatorics

2010 Mathematics Subject Classification

Primary 05A17. Secondary 05A15, 05A19, 11P81.

Received 1 April 2020

Accepted 13 July 2020

Published 16 July 2021