{"id":"hexagon/2610.00324","pdf":"https://hexagonmath.org/pdf/2610.00324v1","url":"https://hexagonmath.org/abs/2610.00324v1","tags":["msc:05A05","Lean formalization","Stirling permutations","lucky sets","parking functions"],"score":0,"title":"Three-Element Lucky Sets of Stirling Permutations","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["YURAN XIU"],"reviews":0,"subject":"math.CO","summary":"We characterize the three-element sets of lucky car indices that occur when a Stirling permutation of order $n$ is used as a parking function. A set $\\{1,x,y\\}$, with $1<x<y<2n$, is admissible precisely when $x$ is odd, or $x$ is even and $y$ is odd with $x<n$, or both are even with $x+y\\leq2n$. Explicit Stirling words realize every permitted case. The number of admissible sets is $(n-1)(n-2)+2nh-3h(h+1)/2$, where $h=\\lfloor(n-1)/2\\rfloor$. This answers the three-element characterization and enumeration question in Problem 46 of Colmenarejo et al. The complete classification, parking…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-18","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}