Turán Densities for Small Hypercubes
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909682065473536 |
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| author | Ellis, David Ivan, Maria-Romina Leader, Imre |
| author_facet | Ellis, David Ivan, Maria-Romina Leader, Imre |
| contents | How small can a set of vertices in the $n$-dimensional hypercube $Q_n$ be if it meets every copy of $Q_d$? The asymptotic density of such a set (for $d$ fixed and $n$ large) is denoted by $γ_d$. It is easy to see that $γ_d \leq 1/(d+1)$, and it is known that $γ_d=1/(d+1)$ for $d \leq 2$, but it was recently shown that $γ_d < 1/(d+1)$ for $d \geq 8$. In this paper we show that the latter phenomenon also holds for $d=7$ and $d=6$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09445 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Turán Densities for Small Hypercubes Ellis, David Ivan, Maria-Romina Leader, Imre Combinatorics 05C65 How small can a set of vertices in the $n$-dimensional hypercube $Q_n$ be if it meets every copy of $Q_d$? The asymptotic density of such a set (for $d$ fixed and $n$ large) is denoted by $γ_d$. It is easy to see that $γ_d \leq 1/(d+1)$, and it is known that $γ_d=1/(d+1)$ for $d \leq 2$, but it was recently shown that $γ_d < 1/(d+1)$ for $d \geq 8$. In this paper we show that the latter phenomenon also holds for $d=7$ and $d=6$. |
| title | Turán Densities for Small Hypercubes |
| topic | Combinatorics 05C65 |
| url | https://arxiv.org/abs/2411.09445 |