Inversions in parking functions
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912539340701696 |
|---|---|
| author | Celano, Kyle Elder, Jennifer Hadaway, Kimberly P. Harris, Pamela E. Priestley, Amanda Udell, Gabe |
| author_facet | Celano, Kyle Elder, Jennifer Hadaway, Kimberly P. Harris, Pamela E. Priestley, Amanda Udell, Gabe |
| contents | In this paper, we obtain a q-exponential generating function for inversions on parking functions via symmetric function theory and also through a direct bijection to rooted labeled forests. We then apply these techniques to unit interval parking functions to give analogous results. We conclude by introducing a probabilistic approach through which we obtain formulas for the total number of inversions and several other statistics across all parking functions and other sets of words closed under rearrangement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11587 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inversions in parking functions Celano, Kyle Elder, Jennifer Hadaway, Kimberly P. Harris, Pamela E. Priestley, Amanda Udell, Gabe Combinatorics 05A05, 05E05 In this paper, we obtain a q-exponential generating function for inversions on parking functions via symmetric function theory and also through a direct bijection to rooted labeled forests. We then apply these techniques to unit interval parking functions to give analogous results. We conclude by introducing a probabilistic approach through which we obtain formulas for the total number of inversions and several other statistics across all parking functions and other sets of words closed under rearrangement. |
| title | Inversions in parking functions |
| topic | Combinatorics 05A05, 05E05 |
| url | https://arxiv.org/abs/2508.11587 |