Related papers: On relation between statistical ideal and ideal ge…
In this paper we study ideals generated by quite general sets of 2-minors of an $m \times n$-matrix of indeterminates. The sets of 2-minors are defined by collections of cells and include 2-sided ladders. For convex collections of cells it…
Let $R$ be a commutative ring with the unit element. It is shown that an ideal $I$ in $R$ is pure if and only if Ann$(f)+I=R$ for all $f\in I$. If $J$ is the trace of a projective $R$-module $M$, we prove that $J$ is generated by the…
A brief review is given of the basic observed features of the stellar IMF, and also of some of the theoretical ideas and simulations that may help to explain these features. The characteristic stellar mass of order one solar mass may derive…
We introduce the notion of the difference quotient set of a real valued function $f$ on a set $E\subset[0,1]$, and compare this set to the range of $f$ on $E$. We discuss the measure theoretic properties of both the range and the difference…
This article is concerned with the number of generators of perfect ideals J in regular local rings (R,m). If J is sufficiently large modulo $m^n$, a bound is established depending only on n and the projective dimension of J. More ambitious…
The diffusion probabilistic generative models are widely used to generate high-quality data. Though they can synthetic data that does not exist in the training set, the rationale behind such generalization is still unexplored. In this…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
We count the finitely generated subgroups of the modular group $\textsf{PSL}(2,\mathbb{Z})$. More precisely: each such subgroup $H$ can be represented by its Stallings graph $\Gamma(H)$, we consider the number of vertices of $\Gamma(H)$ to…
The degree excess function $\epsilon(I;n)$ is the difference between the maximal generating degree $d(I^n)$ of a homogeneous ideal $I$ of a polynomial ring and $p(I)n$, where $p(I)$ is the leading coefficient of the asymptotically linear…
With every $\sigma$-ideal $I$ on a Polish space we associate the $\sigma$-ideal $I^*$ generated by the closed sets in $I$. We study the forcing notions of Borel sets modulo the respective $\sigma$-ideals $I$ and $I^*$ and find connections…
In this article, we prove that sequences generated by the functional calculus $(f(T)(e_n))_{n \in \mathbb{N}}$ can be equivalently written as function sequences $(f_n(T) g)_{n \in \mathbb{N}}$, when $T$ is normal and $g$ a cyclic vector for…
In combinatorial commutative algebra and algebraic statistics many toric ideals are constructed from graphs. Keeping the categorical structure of graphs in mind we give previous results a more functorial context and generalize them by…
The propositional logic is generalized on the real numbers field. the logical function with all properties of the classical probability function is obtained. The logical analog of the Bernoulli independent tests scheme is constructed. The…
Interacting systems of particles with generalized statistics are considered on both classical and quantum level. It is shown that all possible quantum states and corresponding processes can be represented in terms of certain specific…
The content of a polynomial $f(t)$ is the ideal generated by its coefficients. Our aim here is to consider a beautiful formula of Dedekind-Mertens on the content of the product of two polynomials, to explain some of its features from the…
We derive modular parametrizations for certain infinite series whose summands involve central binomial coefficients and higher-order harmonic numbers. When the rates of convergence are certain rational numbers, modularity allows us to…
Given a number $q$, we construct a monomial ideal $I$ with the property that the function which describes the number of generators of $I^k$ has at least $q$ local maxima.
We determine sets of elements which, under certain conditions, generate an intersection of ideals up to radical.
In a recent work, we introduced \textit{LC-functions} $L(s,f)$, associated to a certain real-analytic function $f$ at $0$, extending the concept of the Hurwitz zeta function and its formula. In this paper, we establish the existence of a…
We determine the arithmetical rank of every edge ideal of a Ferrers graph.