Asymptotics of the Number of Threshold Functions and the Singularity Probability of Random {±1}-Matrices

Irmatov, Anwar

doi:10.1134/s1064562420030096

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

2024

Publication Types

Select...

Article3

Other1

Relationship

Self Cite0

Independent4

Authors

Journals

Cited by 4 publications

(1 citation statement)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This result is useful in solving problems of enumerative combinatorics. For example, in [2], [3], [4] a special hyperplane arrangement with several related geometric constructions was introduced in order to estimate the number of threshold functions.…”

Section: Introductionmentioning

confidence: 99%

On the matching arrangement of a graph and properties of its characteristic polynomial

Bolotnikov¹

2022

Preprint

View full text Add to dashboard Cite

This paper considers a hyperplane arrangement constructed with a subset of a set of all simple paths in a graph. A connection of the constructed arrangement to the maximum matching problem is established. Moreover, the problem of finding the characteristic polynomial is reduced to the case of a connected initial graph. The formula of the characteristic polynomial was also found for the case, when the initial graph is a tree.

show abstract

Section: Introductionmentioning

confidence: 99%