Related papers: A Note on Formulas Transmuting Mixed Multiplicitie…

Let $ R=k[x_1...x_r]$ and $M$ a multigraded $R-$module. In this work we interpret $M$ as a multipersistent homology module and give a multigraded resolution of it. The construction involves cellular resolutions of monomial ideals and…

A multiplication on persistence diagrams is introduced by means of Schubert calculus. The key observation behind this multiplication comes from the fact that the representation space of persistence modules has the structure of the Schubert…

Let $R$ be a $G$-graded ring. In this article, we introduce two new concepts on graded rings, namely, weakly graded rings and invertible graded rings, and we discuss the relations between these concepts and several properties of graded…

In this work, we shall study in a purely model-independent fashion the $\infty$-category of mixed graded modules over a ring of characteristic $0$, and collect some basic results about its main formal properties. Finally, we shall endow…

This is a review article on mirror symmetry and aspects of it related to the theory of modular forms. We describe this topic along its historical development and connect to some more recent results toward the end. The article is for…

The ring of dual numbers over a ring $R$ is $R[\alpha] = R[x]/(x^2)$, where $\alpha$ denotes $x+(x^2)$. For any finite commutative ring $R$, we characterize null polynomials and permutation polynomials on $R[\alpha]$ in terms of the…

We consider some Diophantine problems of mixed modular-multiplicative type associated with the Zilber-Pink conjecture. In particular, we prove a finiteness statement for the number of multiplicative relations between singular moduli…

Let R be a commutative ring with identity, S be a multiplicatively closed subset of R, and let M be an R-module. The aim of this paper is to introduce the notion of S-secondary submodules of M as a generalization of secondary submodules of…

In this paper, a classification of modules of the intermediate series over the twisted N=2 superconformal algebra is obtained.

This paper is devoted to establishing several new formulas relating Bernoulli and Stirling numbers of both kinds.

In this paper we define a class of braces, that we call module braces or $R$-braces, which are braces for which the additive group has also a module structure over a ring $R$, and for which the values of the gamma functions are…

The set of idempotents of a regular semigroup is given an abstract characterization as a regular biordered set in [2], and in [4] it is shown how a biordered set can be associated with a complemented modular lattice. Von Neumann has shown…

In this article, we revisit some block matrix construction methods and use them to derive various general expansion formulas for calculating the ranks of matrix expressions. As applications, we derive a variety of interesting rank…

We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their persistence modules, and show that they contain equivalent…

We provide a framework connecting several well known theories related to the linearity of graded modules over graded algebras. In the first part, we pay a particular attention to the tensor products of graded bimodules over graded algebras.…

This paper focuses on the specification of the weights for the components of mixture priors.

In this paper, firstly, we mainly study the relationship of balanced pairs among three Abelian categories in a recollement. As an application of admissible balanced pairs, we introduce the notion of the relative tilting modules, and give a…

Let $R$ be a standard graded Noetherian algebra over an Artinian local ring. Motivated by the work of Achilles and Manaresi in intersection theory, we first express the multiplicity of $R$ by means of local $j$-multiplicities of various…

In this note we investigate mixed partitions with extra condition on the sizes of the blocks. We give a general formula and the generating function. We consider in more details a special case, determining the generating functions, some…

We discuss an Ansatz for the neutrino mixing matrix and speculate on the form and origin of the neutrino mass matrix.