Factorization length distribution for affine semigroups I: Numerical semigroups with three generators. (May 2019)

• Record Type: Journal Article
• Authors: Garcia, Stephan Ramon; O'Neill, Christopher; Yih, Samuel
• Is Part Of: European journal of combinatorics. Volume 78(2019)
• Page Start: 190
• Page End: 204
• Publication Date: 2019-05
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2019.01.009
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: Most factorization invariants in the literature extract extremal factorization behavior, such as the maximum and minimum factorization lengths. Invariants of intermediate size, such as the mean, median, and mode factorization lengths are more subtle. We use techniques from analysis and probability to describe the asymptotic behavior of these invariants. Surprisingly, the asymptotic median factorization length is described by a number that is usually irrational.