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Congruence relations satisfied by quaternionic modular forms
The theory of quaternionic modular forms has been studied for decades as an example of the modular forms of many variables. The purpose of this study...
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Finitely based congruence varieties
We show that for a large class of varieties of algebras, the equational theory of the congruence lattices of the members is not finitely based.
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On Rational Algorithms for Recognition of Belonging to Congruence Classes
AbstractThe theory of similarity transformations, which is the main part of square matrix theory, deals with numerous classes of special matrices....
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Congruence relation between Stirling numbers of the first and second kinds
This paper consists of certain congruence properties of Stirling numbers of the first and second kinds. Some congruence relations between s ( n , k ) and S (...
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Growth of k-Dimensional Systoles in Congruence Coverings
We study growth of absolute and homological k -dimensional systoles of arithmetic n -manifolds along congruence coverings. Our main interest is in the...
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Infinitely many new properties of the congruence lattices of slim semimodular lattices
Slim planar semimodular lattices (SPS lattices or slim semimodular lattices for short) were introduced by G. Grätzer and E. Knapp in 2007. More than...
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A single-variable proof of the omega SPT congruence family over powers of 5
In 2018, Liuquan Wang and Yifan Yang proved the existence of an infinite family of congruences for the smallest parts function corresponding to the...
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Congruence Pairs of Decomposable MS-Algebras
In this paper, the authors first introduce the concept of congruence pairs on the class of decomposable MS-algebras generalizing that for principal...
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Kernel and Trace Relations
With this chapter, we initiate a systematic study of the structure of the lattice...
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Congruence Normality of Simplicial Hyperplane Arrangements via Oriented Matroids
A catalogue of simplicial hyperplane arrangements was first given by Grünbaum in 1971. These arrangements naturally generalize finite Coxeter...
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The Bloch–Okounkov theorem for congruence subgroups and Taylor coefficients of quasi-Jacobi forms
There are many families of functions on partitions, such as the shifted symmetric functions, for which the corresponding q -brackets are quasimodular...
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The topological shadow of \({{{\mathbb {F}}}_1}\)-geometry: congruence spaces
In this paper we introduce congruence spaces, which are topological spaces that are canonically attached to monoid schemes and that reflect closed...
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Fully Invariant Relations
We started a systematic study of varieties of completely regular semigroups and the associated lattice...
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Checking the Congruence of Involutive Matrices
A finite computational process using arithmetic operations only is called a rational algorithm. Presently, no rational algorithm for checking the...
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Congruence-Permutable \( S \)-Acts
An algebra is congruence-permutable if its congruences commute under composition. Many familiar varieties of algebras, such as the variety of groups,...
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Relations and Functions
The topic of relations and functions is central in all mathematics and computing. In the former, whether it is calculus, algebra or theory of...
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On further modular relations for the Rogers–Ramanujan functions
In his work, Ramanujan recorded a list of 40 beautiful modular relations for the Rogers–Ramanujan functions (RRFs) G ( q ) and H ( q ) and noted,...