An Erdős-Ko-Rado theorem for binary codes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913033404547072 |
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| author | Asgarli, Shamil Yip, Chi Hoi |
| author_facet | Asgarli, Shamil Yip, Chi Hoi |
| contents | We study intersecting families of words from the Erdős-Ko-Rado perspective. When the alphabet size is $2$, a maximum intersecting family is not necessarily a star. However, we prove that every maximum $3$-wise intersecting family is a star. We also present a new proof of the known result for alphabets of size at least $3$: maximum intersecting families of words are exactly the stars. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13475 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Erdős-Ko-Rado theorem for binary codes Asgarli, Shamil Yip, Chi Hoi Combinatorics 05D05 We study intersecting families of words from the Erdős-Ko-Rado perspective. When the alphabet size is $2$, a maximum intersecting family is not necessarily a star. However, we prove that every maximum $3$-wise intersecting family is a star. We also present a new proof of the known result for alphabets of size at least $3$: maximum intersecting families of words are exactly the stars. |
| title | An Erdős-Ko-Rado theorem for binary codes |
| topic | Combinatorics 05D05 |
| url | https://arxiv.org/abs/2604.13475 |