Related papers: Products of Luzin-type sets with combinatorial pro…

Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…

In this paper, we examine the combinatorial properties of conic arrangements in the complex projective plane that possess certain quasi-homogeneous singularities. First, we introduce a new tool that enables us to characterize the property…

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…

We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the…

We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L^2 torsions which, unlike the work of…

Gaudin algebra is the commutative subalgebra in $U(\mathfrak{g})^{\otimes N}$ generated by higher integrals of the quantum Gaudin magnet chain attached to a semisimple Lie algebra $\mathfrak{g}$. This algebra depends on a collection of…

We generalize a construction in [BW18] (arXiv:1610.09271) by showing that the tensor product of a based $\textbf{U}^{\imath}$-module and a based $\textbf{U}$-module is a based $\textbf{U}^{\imath}$-module. This is then used to formulate a…

A combinatorial construction is used to analyze the properties of polyhedral products and generalized moment-angle complexes with respect to certain operations on CW pairs including exponentiation. This allows for the construction of…

We introduce the notion of additive units and roots of a unit in a spatial product system. The set of all roots of any unit forms a Hilbert space and its dimension is the same as the index of the product system. We show that a unit and all…

We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is…

This paper constructs a combinatorial model for all postcritically finite rational maps arising as the Newton's method of a complex polynomial. This model is used in [LMS] to give a combinatorial classification of postcritically finite…

We investigate the occurrence of additive and multiplicative structures in random subsets of the natural numbers. Specifically, for a Bernoulli random subset of $\mathbb{N}$ where each integer is included independently with probability…

We show that every combinatorial model category can be obtained, up to Quillen equivalence, by localizing a model category of diagrams of simplicial sets. This says that any combinatorial model category can be built up from a category of…

We prove that in the Miller model the Menger property is preserved by finite products of metrizable spaces. This answers several open questions and gives another instance of the interplay between classical forcing posets with fusion and…

We adapt methods coming from additive combinatorics in groups to the study of linear span in associative unital algebras. In particular, we establish for these algebras analogues of Diderrich-Kneser's and Hamidoune's theorems on sumsets and…

We propose and investigate a bi-infinite matrix approach to the multiplication and composition of formal Laurent series. We generalize the concept of Riordan matrix to this bi-infinite context, obtaining matrices that are not necessarily…

In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…

We develop a method that we call \emph{omission of intervals}, for establishing topological properties of subsets of the real line based on their combinatorial structure. Using this method, we obtain conceptual proofs of the fundamental…

In this paper, we continue the study of linear sets with complementary weights. We find criteria to determine the set of points of any fixed weight and use this to present particular linear sets with few points of weight more than one. We…

We incorporate a category of certain modules for an affine Lie algebra, of a certain fixed non-positive-integral level, considered by Kazhdan and Lusztig, into the representation theory of vertex operator algebras, by using the logarithmic…