TL;DR
This paper introduces an involution on set partitions that swaps two statistics related to block sizes, leading to an equidistribution result for objects counted by Bessel numbers.
Contribution
It presents a novel involution on set partitions that connects two statistics and proves their equidistribution with respect to Bessel numbers.
Findings
Established an involution interchanging block size statistics
Proved equidistribution of statistics for set partitions
Connected set partition statistics to Bessel numbers
Abstract
We present an involution on set partitions that interchanges two statistics related to relative size of block entries and use it to establish an equidistribution on objects counted by the Bessel numbers.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Statistical Methods and Models · Advanced Mathematical Identities · Advanced Combinatorial Mathematics