Journal of Integer Sequences, Vol. 28 (2025), Article 25.5.2

An Exceptional Equinumerosity of Lattice Paths and Young Tableaux


Liam Ayres
Department of Pure Mathematics
University of Waterloo
Waterloo, ON N2L 3G1
Canada

Evan Bialo
Department of Statistics & Actuarial Science
University of Waterloo
Waterloo, ON N2L 3G1
Canada

Alwin Chen and Aidan Cook
Department of Pure Mathematics
University of Waterloo
Waterloo, ON N2L 3G1
Canada

Matteus Froese, Erica Liu, Maryam Mohammadi Yekta, Oliver Pechenik, and Benjamin Wong
Department of Combinatorics & Optimization
University of Waterloo
Waterloo, ON N2L 3G1
Canada

Abstract:

We consider families 𝒫n of plane lattice paths enumerated by Guy, Krattenthaler, and Sagan. We show by explicit bijection that these families are equinumerous with the set SYT(n + 2, 2, 1n) of standard Young tableaux.

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(Concerned with sequence A253487.)

Received June 19 2025; revised versions received September 13 2025; September 14 2025. Published in Journal of Integer Sequences, September 15 2025.

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