Combinatorics of Multicompositions

@article{Hopkins2020CombinatoricsOM,
  title={Combinatorics of Multicompositions},
  author={Brian Hopkins and St'ephane Ouvry},
  journal={arXiv: Combinatorics},
  year={2020}
}
Integer compositions with certain colored parts were introduced by Andrews in 2007 to address a number-theoretic problem. Integer compositions allowing zero as some parts were introduced by Ouvry and Polychronakos in 2019. We give a bijection between these two varieties of compositions and determine various combinatorial properties of these multicompositions. In particular, we determine the count of multicompositions by number of all parts, number of positive parts, and number of zeros. Then… 

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