Séminaire Lotharingien de Combinatoire, 95B.47 (2026), 12 pp.
Zachary Hamaker and Jesse Kim
Odd Shifted Parking Functions
Abstract.
Stanley recently introduced the shifted parking function symmetric
function SHn as the shiftification of Haiman's
parking function symmetric function PFn.
The function SHn lives in the subalgebra of
symmetric functions generated by odd power sums.
Stanley showed how to expand SHn into
the V-basis of this algebra, which is indexed by partitions
with all parts odd and is analogous to the complete homogeneous (or
elementary) basis of symmetric functions.
We introduce odd shifted parking functions to give
combinatorial and representation-theoretic realizations of
the V-expansion of SHn, resolving the main
open problem in his paper.
We conclude with further directions, including a relationship between
SHn and Haglund's (q,t)-Schröder theorem.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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