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Set Theory

Oberwolfach Reports, 2023
Set theory has experienced rapid development in the recent years, both in pure set theory and in its applications to other fields of mathematics. We have seen breakthroughs in combinatorial set theory, forcing, inner models, descriptive set theory, Borel
Ilijas Farah   +3 more
semanticscholar   +1 more source

A Generalization of the Chevalley–Warning and Ax–Katz Theorems with a View Towards Combinatorial Number Theory

Combinatorica, 2022
Let $${\mathbb {F}}_q$$ F q be a finite field of characteristic p and order q . The Chevalley–Warning Theorem asserts that the set V of common zeros of a collection of polynomials must satisfy $$|V|\equiv 0\mod p$$ | V | ≡ 0 mod p , provided the number ...
D. Grynkiewicz
semanticscholar   +1 more source

Combinatorial Complexes: Bridging the Gap Between Cell Complexes and Hypergraphs

Asilomar Conference on Signals, Systems and Computers, 2023
Graph-based signal processing techniques have be-come essential for handling data in non-Euclidean spaces. How-ever, there is a growing awareness that these graph models might need to be expanded into ‘higher-order’ domains to effectively represent the ...
Mustafa Hajij   +5 more
semanticscholar   +1 more source

Multi-antenna Coded Caching with Combinatorial Multi-access Networks

International Symposium on Information Theory, 2023
We study the combinatorial multi-access coded caching problem, introduced by Muralidhar et al. with a single antenna at the server [P. N. Muralidhar, D. Katyal, and B. S. Rajan, "Maddah-Ali-Niesen scheme for multi-access coded caching," in IEEE ITW, 2021]
Elizabath Peter, B. Rajan
semanticscholar   +1 more source

Combinatorial-Probabilistic Trade-Off: P-Values of Community Property Test in the Stochastic Block Models

IEEE Transactions on Information Theory, 2023
In this paper, we propose an inferential framework testing the general community combinatorial properties of the stochastic block model. Instead of estimating the community assignments, we aim to test the hypothesis on whether a certain community ...
Shuting Shen, Junwei Lu
semanticscholar   +1 more source

Employing the Erdős–Ko–Rado theorem to develop new techniques in combinatorial intersection theory

Journal of Discrete Mathematical Sciences & Cryptography
The Erdūs–Ko–Rado (EKR) theorem is a renowned result in combinatorial mathematics. It tells a lot about cross-set groups. This study examines how the EKR theorem might inspire combinatorial intersection theory concepts. By studying the EKR theorem’s core
Sheela Hundekari   +5 more
semanticscholar   +1 more source

Combinatorial Set Theory: Partition Relations for Cardinals

, 2012
N. H. Williams   +4 more
semanticscholar   +1 more source

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