Séminaire Lotharingien de Combinatoire, 95B.32 (2026), 12 pp.
Michele D'Adderio and Alessio Sgubin
A Loehr-Remmel Bijection in the n × kn grid
Abstract.
We extend the pmaj statistic of Loehr and Remmel to labelled Dyck
paths in the n × kn grid, and extend their
bijection sending the bistatistic (dinv,area) to (area,pmaj), proving
in this way a new combinatorial formula for
∇ken (k ≥ 1). At
k = 1 we recover the original statistic and the original bijection.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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