Positivity and negativity for additive h-bases for n

Abstract: A finite set $A$ of integers is an $h$-basis for $n$ if every integer in the interval of integers $\{0,1,2,\ldots, n\}$ can be represented as the sum of exactly $h$ not necessarily distinct elements of $A$. In additive number theory, attention has focused on sets of nonnegative integers, but one can also consider sets that contain negative integers and investigate the effects of ``negativity'' on the classical problem of extremal properties of $h$-bases for $n$. There are new results and a new class of problems for additive bases that contain both positive and negative integers.

commutative algebracombinatoricsnumber theory

Audience: researchers in the topic

New York Number Theory Seminar

Series comments: Meeting ID: 840 6618 4717 Passcode: 304403