New bijections from $n$-color compositions

Combinatorial bijections are given from the set of $n$-color compositions of $\nu$, for which a part of size $n$ can take on $n$ colors, to the set of compositions of $2\nu-1$ having only parts of size 1 or 2, the set of compositions of $2\nu$ having only odd parts, and the set of compositions of $2\nu+1$ having no parts of size 1. A generalized bijection based on similar ideas is then given between the set of compositions of $\nu$ into parts congruent to $a(\text{mod } b)$ and the set of compositions of $\nu+b-a$ into parts congruent to $b(\text{mod } a)$ with each part greater than $b-a$.

Keywords

integer compositions, restricted compositions, $n$-color compositions, Fibonacci numbers

2010 Mathematics Subject Classification

Primary 05A19. Secondary 11B39.

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Published 13 August 2013