Vol. 9, No. 2, 2020

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Generalized colored circular palindromic compositions

Petros Hadjicostas

Vol. 9 (2020), No. 2, 173–186
DOI: 10.2140/moscow.2020.9.173

We derive the generating function (g.f.) of the number of colored circular palindromic compositions of N with K parts in terms of the g.f. of an input sequence a that determines how many different colors each part of the composition can have. As a result, we get the g.f. of the number of all colored circular palindromic compositions of N. Using the latter formula and the g.f. of the number of colored circular compositions, we may easily derive the g.f. of the number of all colored dihedral compositions of N.

circular palindrome, dihedral composition, generating function
Mathematical Subject Classification 2010
Primary: 05A10, 05A15, 11B39
Received: 5 March 2020
Revised: 23 June 2020
Accepted: 12 July 2020
Published: 7 August 2020
Petros Hadjicostas
Department of Mathematical Sciences
University of Nevada
Las Vegas, NV
United States