Year: 2026
Type: article
Abstract: We study lucky cars in subsets of parking functions, called Fubini rankings and unit Fubini rankings. A Fubini ranking is a sequence of nonnegative integers that encodes a valid ranking of competitors, where ties are allowed. A car (or competitor) is said to be lucky if it is the first instance of that rank appearing in the sequence. We present combinatorial characterizations and enumeration formulas for lucky cars in both Fubini rankings and unit Fubini rankings, and establish connections between these objects and ordered set partitions, as well as integer compositions. To obtain our results, we use several techniques to enumerate statistics over these families of objects. In particular, we employ generating functions, bijective and combinatorial arguments, and recurrence relations.
Authors: Camilo Barreto, Melissa Beerbower, Jennifer Elder, Pamela E. Harris, Lucy Martinez, José L. Ramírez, Samuel Ramírez, Grant Shirley, Julio C. Vásqez
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4415926845