Unique sums and differences in finite Abelian groups

• Main Authors: Leung, Ka Hin, Schmidt, Bernhard
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2022
• Subjects: Science::Mathematics; Finite Abelian Groups; Sumsets
• Online Access: https://hdl.handle.net/10356/159769
• Institution: Nanyang Technological University

Let A,B be subsets of a finite abelian group G. Suppose that A+B does not contain a unique sum, i.e., there is no g∈G with a unique representation g=a+b, a∈A, b∈B. From such sets A,B, sparse linear systems over the rational numbers arise. We obtain a new determinant bound on invertible submatrices o...