On the Lucky and Displacement Statistics of Stirling Permutations

Dorian Smith
PhD Student
University of Minnesota Twin Cities

Stirling permutations are parking functions. We investigate two parking function statistics in the context of these objects: lucky cars and displacement. Among our results, we consider two extreme cases: extremely lucky Stirling permutations (those with maximally many lucky cars) and extremely unlucky Stirling permutations (those with exactly one lucky car). We show that the number of extremely lucky Stirling permutations of order n is the Catalan number, and the number of extremely unlucky Stirling permutations is (n−1)!.

This is a joint work with Laura Colmenarejo, Aleyah Dawkins, Jennifer Elder, Pamela E. Harris, Kimberly J.Harry, Selvi Kara, and Bridget Eileen Tenner.