On the Smallest Support Size of Integer Solutions to Linear Equations
Abstract
In this note, we study the size of the support of integer solutions to linear equations Ax=b, ~x∈n where A∈m× n, b∈n. We give an upper bound on the smallest support size as a function of A, taken as a worst case over all b such that the above system has a solution. This bound is asymptotically tight, and in fact matches the bound given in Aliev, Averkov, De Loera and Oertel Mathematical Programming 2022, while the proof presented here is simpler, relying only on linear algebra.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.