Sean Li




Thursday, January 26, 2023 - 10:00am to 11:00am


Zoom: https://uci.zoom.us/j/94729574163

A numerical semigroup Λ is a subset of the nonnegative integers which contains 0, has finite complement, and is closed under addition. We characterize Λ by a number of invariants: the genus g = |N0 \ Λ|, the multiplicity m = min(Λ \ {0}), and the Frobenius number f = max(N0 \ Λ). Recently, Eliahou and Fromentin introduced the notion of depth q = ⌈(f+1)/q⌉. In 1990, Backelin showed that the number of numerical semigroups with Frobenius number f approaches Ci · 2^(f/2) for constants C0 and C1 depending on the parity of f. In this talk, we use Kunz words and graph homomorphisms to generalize Backelin’s result to numerical semigroups of arbitrary Frobenius number, multiplicity, and depth, in particular showing that there are ⌊(q+1)^2/4⌋^(f/(2q-2)+o(f)) semigroups with Frobenius number f and depth q.