A discrete variation of the Littlewood-Offord problem

DOI10.37236/11956arXiv2103.13489OpenAlexW4392035500MaRDI QIDQ6194235

Hossein Esmailian, Ebrahim Ghorbani

Publication date: 19 March 2024

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.13489

zbMATH Keywords

Sperner's theoremrank-order problems for graphs

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Random matrices (algebraic aspects) (15B52) Structural characterization of families of graphs (05C75) Vector spaces, linear dependence, rank, lineability (15A03)

Cites Work

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• Inverse Littlewood-Offord problems for quasi-norms
• The maximum order of adjacency matrices of graphs with a given rank
• On graphs with multiple eigenvalues
• On order and rank of graphs
• Maximum order of trees and bipartite graphs with a given rank
• Star partitions and regularity in graphs
• Maximum order of graphs with a given corank
• Singularity of random Bernoulli matrices
• Inverse Littlewood-Offord theorems and the condition number of random discrete matrices
• The Littlewood-Offord problem and invertibility of random matrices
• On a lemma of Littlewood and Offord on the distribution of certain sums
• On a lemma of Littlewood and Offord on the distributions of linear combinations of vectors
• ON A PROBLEM RELATED TO ONE OF LITTLEWOOD AND OFFORD
• ON THE MULTIPLICITIES OF GRAPH EIGENVALUES
• On the distribution of sums of residues
• The rank and size of graphs
• Maximum Order of Triangle‐Free Graphs with a Given Rank
• On a lemma of Littlewood and Offord

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