Factorization length distribution in numerical semigroups

02/27/2018 - 12:15pm
02/27/2018 - 1:10pm
Samuel Yih (Pomona College)

A numerical semigroup is a cofinite subset of the nonnegative integers closed under addition. Extreme factorization invariants such as the maximum and minimum factorization lengths are well understood, but intermediate invariants such as the mean, median, and mode factorization lengths are more subtle. In this talk we will first study these invariants for semigroups of embedding dimension 3, in which a number of interesting phenomena already occur. We will then broaden our perspective to semigroups of any dimension, for which we have a general result for the mean factorization length and open conjectures for the remaining invariants. Joint work with Stephan Garcia (Pomona College) and Christopher O'Neill (UC Davis).

Millikan 2099, Pomona College

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