Geodesic
A discrete variation of the Littlewood-Offord problem
The electronic journal of combinatorics, Tome 31 (2024) no. 1
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The 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 the Littlewood-Offord 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 $A(G)+I$.
DOI : 10.37236/11956
Classification : 05C50, 05C75, 15A03, 15B52
Mots-clés : Sperner's theorem, rank-order problems for graphs 
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     author = {Hossein  Esmailian and Ebrahim Ghorbani},
     title = {A discrete variation of the {Littlewood-Offord} problem},
     journal = {The electronic journal of combinatorics},
     year = {2024},
     volume = {31},
     number = {1},
     doi = {10.37236/11956},
     zbl = {1535.05168},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/11956/}
}
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Hossein  Esmailian; Ebrahim Ghorbani. A discrete variation of the Littlewood-Offord problem. The electronic journal of combinatorics, Tome 31 (2024) no. 1. doi: 10.37236/11956

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