The $(s,s+d,\dots,s+pd)$-core partitions and the rational Motzkin paths

Hyunsoo Cho; JiSun Huh; Jaebum Sohn

The $(s,s+d,\dots,s+pd)$-core partitions and the rational Motzkin paths

Combinatorics 2020-02-05 v2

Authors: Hyunsoo Cho , JiSun Huh , Jaebum Sohn

Abstract

In this paper, we propose an $(s+d,d)$ -abacus for $(s,s+d,\dots,s+pd)$ -core partitions and establish a bijection between the $(s,s+d,\dots,s+pd)$ -core partitions and the rational Motzkin paths of type $(s+d,-d)$ . This result not only gives a lattice path interpretation of the $(s,s+d,\dots,s+pd)$ -core partitions but also counts them with a closed formula. Also we enumerate $(s,s+1,\dots,s+p)$ -core partitions with $k$ corners and self-conjugate $(s,s+1,\dots,s+p)$ -core partitions.

Keywords

core partitions rational motzkin paths abacus bijection lattice paths closed formula self-conjugate partitions

Cite

@article{arxiv.2001.06651,
  title  = {The $(s,s+d,\dots,s+pd)$-core partitions and the rational Motzkin paths},
  author = {Hyunsoo Cho and JiSun Huh and Jaebum Sohn},
  journal= {arXiv preprint arXiv:2001.06651},
  year   = {2020}
}

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11 pages

The $(s,s+d,\dots,s+pd)$-core partitions and the rational Motzkin paths

Abstract

Keywords

Cite

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