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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.08221 |
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| _version_ | 1866914913470906368 |
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| author | Frankl, Peter Kupavskii, Andrey |
| author_facet | Frankl, Peter Kupavskii, Andrey |
| contents | Let us consider a collection $\mathcal G$ of codewords of length $n$ over an alphabet of size $s$. Let $t_1,\ldots, t_s$ be nonnegative integers. What is the maximum of $|\mathcal G|$ subject to the condition that any two codewords should have at least $t_i$ positions where both have letter $i$ ($1\le i\le s$). In the case $s=2$ it is a longstanding open question. Quite surprisingly, we obtain an almost complete answer for $s\ge 3$. The main tool is a correlation inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08221 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Intersection problems and a correlation inequality for integer sequences Frankl, Peter Kupavskii, Andrey Combinatorics Let us consider a collection $\mathcal G$ of codewords of length $n$ over an alphabet of size $s$. Let $t_1,\ldots, t_s$ be nonnegative integers. What is the maximum of $|\mathcal G|$ subject to the condition that any two codewords should have at least $t_i$ positions where both have letter $i$ ($1\le i\le s$). In the case $s=2$ it is a longstanding open question. Quite surprisingly, we obtain an almost complete answer for $s\ge 3$. The main tool is a correlation inequality. |
| title | Intersection problems and a correlation inequality for integer sequences |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.08221 |