Enumeration of subsets with closedness in finite fields of characteristic 2

2025/06/25 by R, Nithish Kumar, R., Vadiraja Bhatta G., Poojary, Prasanna
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.20351

Abstract

The additive closedness in the subset of an additive group is termed as r-value. The nature of closedness in different subsets of fixed size is observed as a spectrum of r-values. We enumerate r-values of subsets in finite fields of characteristic 2 and represent them as the spectrum of values. Based on these values the subsets can be further studied as partial Steiner triple systems, sum-free sets, Sidon sets, and Schure triples.

Citations

• On sum-free subsets of abelian groups
• Shape of the asymptotic maximum sum-free sets in integer lattice grids
• Regular saturated graphs and sum-free sets
• Minimum number of additive tuples in groups of prime order
• Sumfree sets in groups: a survey
• Beyond sum-free sets in the natural numbers
• Generalized Sidon sets

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