Factorization length distribution for affine semigroups I: numerical semigroups with three generators
Commutative Algebra
2021-02-05 v2 Combinatorics
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.
Keywords
Cite
@article{arxiv.1804.05135,
title = {Factorization length distribution for affine semigroups I: numerical semigroups with three generators},
author = {Stephan Ramon Garcia and Christopher O'Neill and Samuel Yih},
journal= {arXiv preprint arXiv:1804.05135},
year = {2021}
}
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17 pages