Journal article
CARDINALITIES OF g-DIFFERENCE SETS
Integers, v 25, A77
2025
Abstract
Let ηg(n) be the smallest cardinality that A ⊆ Z can have if A is a g-difference basis for [n], i.e, if, for each x ∈ [n], there are at least g solutions to a1−a2 = x. We prove that the finite, non-zero limit lim ηg(n) √ n→∞ n exists, answering a question of Kravitz. We also investigate a similar problem in the setting of a vector space over a finite field. Let αg(n) be the largest cardinality that A ⊆ [n] can have if, for all nonzero x, a1 −a2 = x has at most g solutions. We also prove that αg(n) = √gn(1+og(1)) as n →∞.
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Details
- Title
- CARDINALITIES OF g-DIFFERENCE SETS
- Creators
- Eric Schmutz - Drexel UniversityMichael Tait - Villanova University
- Publication Details
- Integers, v 25, A77
- Grant note
- DMS-2245556 / National Science Foundation (http://data.elsevier.com/vocabulary/SciValFunders/100000001) DMS-2245556 / National Science Foundation (100000001)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- [Retired Faculty]; Mathematics
- Scopus ID
- 2-s2.0-105014293206
- Other Identifier
- 991022197420204721