A Discrete Variation of Littlewood--Offord Problem
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866910303133892608 |
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| author | Esmailian, Hossein Ghorbani, Ebrahim |
| author_facet | Esmailian, Hossein Ghorbani, Ebrahim |
| contents | Littlewood--Offord Problem concerns the number of subsums of a set of vectors that fall in a given convex set. We present a discrete variation of this problem where we estimate the number of subsums that are $(0,1)$-vectors.
We then utilize this to find the maximum order of graphs with given rank or corank. The rank of a graph $G$ is the rank of its adjacency matrix $A(G)$ and the corank of $G$ is the rank of $A(G)+I$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2103_13489 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A Discrete Variation of Littlewood--Offord Problem Esmailian, Hossein Ghorbani, Ebrahim Combinatorics 05C50, 05C75, 15A03 Littlewood--Offord Problem concerns the number of subsums of a set of vectors that fall in a given convex set. We present a discrete variation of this problem where we estimate the number of subsums that are $(0,1)$-vectors. We then utilize this to find the maximum order of graphs with given rank or corank. The rank of a graph $G$ is the rank of its adjacency matrix $A(G)$ and the corank of $G$ is the rank of $A(G)+I$. |
| title | A Discrete Variation of Littlewood--Offord Problem |
| topic | Combinatorics 05C50, 05C75, 15A03 |
| url | https://arxiv.org/abs/2103.13489 |