A Shifted Parking Function Symmetric Function

2024/05/03 by Richard P. Stanley, Stanley, Richard P. · 1 citation
Computer Science · Engineering · #05A15 (Secondary) #05E05 (Primary) #Combinatorics (math.CO) #FOS: Mathematics #Robotic Path Planning Algorithms #Smart Parking Systems Research

paper · pdf · doi:10.48550/arxiv.2405.02164

openalex publication_date 2024/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a "shifted analogue" SH_n of the parking function symmetric function PF_n. The expansion of SH_n in terms of three bases for shifted symmetric functions is explicitly described. We don't know a shifted analogue for parking functions themselves, but some desirable properties of such an analogue are discussed.

Cited by

• Odd Shifted Parking Functions

Related

• Odd Shifted Parking Functions
• A Hopf algebra of parking functions
• Inversions in parking functions
• Parking functions and Haglund--Loehr data
• Bounded Height Interlaced Pairs of Parking Functions