An exceptional equinumerosity of lattice paths and Young tableaux

Liam Ayres; Evan Bialo; Aidan Cook; Alwin Chen; Matteus Froese; Erica Liu; Maryam Mohammadi Yekta; Oliver Pechenik; Benjamin Wong

An exceptional equinumerosity of lattice paths and Young tableaux

Combinatorics 2025-06-04 v1

Authors: Liam Ayres , Evan Bialo , Aidan Cook , Alwin Chen , Matteus Froese , Erica Liu , Maryam Mohammadi Yekta , Oliver Pechenik , Benjamin Wong

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Abstract

We consider families $\mathcal{P}_n$ of plane lattice paths enumerated by Guy, Krattenthaler, and Sagan (1992). We show by explicit bijection that these families are equinumerous with the set $\mathrm{SYT}(n+2,2,1^n)$ of standard Young tableaux.

Keywords

lattice paths Young tableaux equinumerosity bijection standard Young tableaux combinatorics

Cite

@article{arxiv.2506.03116,
  title  = {An exceptional equinumerosity of lattice paths and Young tableaux},
  author = {Liam Ayres and Evan Bialo and Aidan Cook and Alwin Chen and Matteus Froese and Erica Liu and Maryam Mohammadi Yekta and Oliver Pechenik and Benjamin Wong},
  journal= {arXiv preprint arXiv:2506.03116},
  year   = {2025}
}

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7 pages, 1 figure

An exceptional equinumerosity of lattice paths and Young tableaux

Abstract

Keywords

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