A Bijection between Two Classes of Restricted Compositions

Document Type

Article

Publication Date

2012

Publication Title

Fibonacci Quarter

Abstract

Two proofs, one using generating functions, the other bijective, are given for the following theorem: The number of compositions of n into parts congruent to 1 (mod k) equals the number of compositions of n + k − 1 into parts greater than k − 1. This bijection is then proven to hold for palindromic compositions. A more general theorem is presented in conclusion.

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