Bijective counting of humps and peaks in $(k,a)$-paths

Sherry H. F. Yan

Bijective counting of humps and peaks in $(k,a)$-paths

Combinatorics 2014-06-12 v2

Authors: Sherry H. F. Yan

Abstract

Recently, Mansour and Shattuck related the total number of humps in all of the $(k, a)$ -paths of order $n$ to the number of super $(k, a)$ -paths, which generalized previous results concerning the cases when $k = 1$ and $a = 1$ or $a = \infty$ . They also derived a relation on the total number of peaks in all of the $(k, a)$ -paths of order $n$ and the number of super $(k, a)$ -paths, and asked for bijective proofs. In this paper, we will give bijective proofs of these two relations.

Keywords

bijective proofs humps peaks (k,a)-paths super (k,a)-paths combinatorics counting

Cite

@article{arxiv.1304.0351,
  title  = {Bijective counting of humps and peaks in $(k,a)$-paths},
  author = {Sherry H. F. Yan},
  journal= {arXiv preprint arXiv:1304.0351},
  year   = {2014}
}

Comments

This is the revised version

Bijective counting of humps and peaks in $(k,a)$-paths

Abstract

Keywords

Cite

Comments

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