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The Expected Embedding Dimension, type and weight of a Numerical Semigroup
Nathan Kaplan, Deepesh Singhal
We study statistical properties of numerical semigroups of genus as goes to infinity. More specifically, we answer a question of Eliahou by showing that as goes to infi…
Frobenius allowable gaps of Generalized Numerical Semigroups
Deepesh Singhal, Yuxin Lin
A generalised numerical semigroup (GNS) is a submonoid of for which the complement is finite. The points in the complement $\mathbb{N}^…
Complementary Numerical Sets
Matthew Guhl, Jazmine Juarez, Vadim Ponomarenko +2
A numerical set is a cofinite subset of which contains . We use the natural bijection between numerical sets and Young diagrams to define a numerical set $\wide…
Distribution of genus among numerical semigroups with fixed Frobenius number
Deepesh Singhal
A numerical semigroup is a sub-semigroup of the natural numbers that has a finite complement. The size of its complement is called the genus and the largest number in the complemen…