相关论文: The combinatorics of Borel covers

We survey and analyze different ways in which bornologies, coarse structures and uniformities on a group agree with the group operations.

The aim of this paper is to introduce Bell polynomials and numbers of the second kind and poly-Bell polynomials and numbers of the second kind, and to derive their explicit expressions, recurrence relations and some identities involving…

This work is a survey on completely regular codes. Known properties, relations with other combinatorial structures and constructions are stated. The existence problem is also discussed and known results for some particular cases are…

A construction of new sequences of generalized Bernoulli polynomials of first and second kind is proposed. These sequences share with the classical Bernoulli polynomials many algebraic and number--theoretical properties. A new class of…

We prove that many seemingly simple theories have Borel complete reducts. Specifically, if a countable theory has uncountably many complete 1-types, then it has a Borel complete reduct. Similarly, if $Th(M)$ is not small, then $M^{eq}$ has…

We classify Borel-Schur algebras having finite representation type. We also de- termine Auslander-Reiten sequences for a large class of simple modules over Borel- Schur algebras. A partial information on the structure of the socles of…

In this paper we continue to investigate a certain class of Hankel-like positive definite kernels using their associated orthogonal polynomials. The main result of this paper is about the structure of this kind of kernels.

Let $\pi\colon \mathcal{X}\to B$ be a family whose general fiber $X_b$ gives a $(d_1,...,d_a)$ polarisation of a general Abelian variety where $1\leq d_i\leq 2$, $i=1,...,a$ and $a\geq 4$. We show that the fibers are in the same birational…

This paper concerns the characterisation of second order marginals for random sets in a discrete setting. Under the instance of unit covariances, this problem possesses a combinatorial symmetry, exploited jointly in the companion paper to…

An extension of order theory is presented that serves as a formalism for the study of dendroidal sets analogously to way the formalism of order theory is used in the study of simplicial sets.

In this paper we define the combinatorial analogous of a pencil, and show its relationship with the concept of admissibility. Such an object is usefull to study the isomorphisms between fundamental groups of the complements of line…

We classify essential algebras whose irredundant non-refinable covers consist of primal algebras. The proof is obtained by constructing one to one correspondence between such algebras and partial orders on finite sets. Further, we prove…

In a series of papers, P. Blasiak et al. developed a wide-ranging generalization of Bell numbers (and of Stirling numbers of the second kind) that appears to be relevant to the so-called Boson normal ordering problem. They provided a…

Let k be an algebraically closed field of characteristic p>0. We compute the Weyl filtration multiplicities in indecomposable tilting modules and the decomposition numbers for the general linear group over k in terms of cap diagrams under…

This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and…

In this note a combinatorial formula related to the symmetric group is generalized to an arbitrary finite Weyl group.

A combinatorial characterization of measurable filters on a countable set is found. We apply it to the problem of measurability of the intersection of nonmeasurable filters.

The paper presents several combinatorial properties of the boolean cumulants. A corollary is a new proof of the multiplicative property of the boolean cumulant series that can be easily adapted for the case of boolean independence with…

In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.

In this paper, we propose a new type of matroids, namely covering matroids, and investigate the connections with the second type of covering-based rough sets and some existing special matroids. Firstly, as an extension of partitions,…