Enumeration of subsets with closedness in finite fields of characteristic 2
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915358432034816 |
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| author | R, Nithish Kumar R., Vadiraja Bhatta G. Poojary, Prasanna |
| author_facet | R, Nithish Kumar R., Vadiraja Bhatta G. Poojary, Prasanna |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20351 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enumeration of subsets with closedness in finite fields of characteristic 2 R, Nithish Kumar R., Vadiraja Bhatta G. Poojary, Prasanna Combinatorics 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. |
| title | Enumeration of subsets with closedness in finite fields of characteristic 2 |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.20351 |