A Polynomial Bosonic Form of Statistical Configuration Sums and the Odd/Even Minimal Excludant in Integer Partitions
Abstract
Inspired by the study of the minimal excludant in integer partitions by G.E. Andrews and D. Newman, we introduce a pair of new partition statistics, sqrank and rerank. They are related to a polynomial bosonic form of statistical configuration sums for an integrable cellular automaton. For all non-negative integers n, we prove that the partitions of n on which sqrank or rerank takes on a particular value, say r, are equinumerous with the partitions of n on which the odd/even minimal exclutant takes on the corresponding value, $$2r+1$$ or $$2r+2$$ .
Fields of Study & Subjects
Advanced Mathematical Identities
Advanced Statistical Methods and Models
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Annals of Combinatorics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 30
- Issue
- 3
- Pages
- 817–847
- Publication date
- 6 February 2026
- Language
- EN