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Sets Characterized by Missing Sums and Differences
Yufei Zhao
A more sums than differences (MSTD) set is a finite subset S of the integers such |S+S| > |S-S|. We show that the probability that a uniform random subset of {0, 1, ..., n} is an M…
Counting MSTD Sets in Finite Abelian Groups
Yufei Zhao
In an abelian group G, a more sums than differences (MSTD) set is a subset A of G such that |A+A|>|A-A|. We provide asymptotics for the number of MSTD sets in finite abelian groups…
Constructing Numerical Semigroups of a Given Genus
Yufei Zhao
Let n_g denote the number of numerical semigroups of genus g. Bras-Amoros conjectured that n_g possesses certain Fibonacci-like properties. Almost all previous attempts at proving…
Constructing MSTD Sets Using Bidirectional Ballot Sequences
Yufei Zhao
A more sums than differences (MSTD) set is a finite subset S of the integers such that |S+S| > |S-S|. We construct a new dense family of MSTD subsets of {0, 1, 2, ..., n-1}. Our co…