New bijections from $n$-color compositions
Caroline Shapcott · Journal of Combinatorics · 2013
Combinatorial bijections are given from the set of n-color compositions of ν, for which a part of size n can take on n colors, to the set of compositions of 2ν -1 having only parts of size 1 or 2, the set of compositions of 2ν having only odd parts, and the set of compositions of 2ν + 1 having no parts of size 1.A generalized bijection based on similar ideas is then given between the set of compositions of ν into parts congruent to a(mod b) and the set of compositions of ν + ba into parts congruent to b(mod a) with each part greater than ba.