Experimental Mathematics· 2026Q1
The Thirty-Seven Measures on Permutations
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- Q1SCImago
- 2026year
Short summary
Exactly 37 measures exist on the class of permutations, with two yielding a new pre-Tannakian tensor category.
AI-generated from the title and abstract; the full text is not read.
Key points
- Identified exactly 37 measures on the class of permutations.
- Utilized Nekrasov's method and computer calculations for the analysis.
- Two of these measures define a new pre-Tannakian tensor category.
AI-generated from the title and abstract; the full text is not read.
Abstract
In recent work with Harman, we introduced a notion of measure on a class of finite relational structures. In this note, we consider measures on the class of permutations, i.e., finite sets with two total orders. Using a method of Nekrasov, and some computer calculations, we show that there are exactly 37 measures. Two of these measures lead to a new pre-Tannakian tensor category.
The authors' abstract, as published at the source. Experimental Mathematics, 2026 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics