相关论文: On cobweb posets and their combinatorially admissi…

We define a family of combinatorial objects, which we call Baxter posets. We prove that Baxter posets are counted by the Baxter numbers by showing that they are the adjacency posets of diagonal rectangulations. Given a diagonal…

In this paper we deal with the feasibility-seeking problem for unions of convex sets (UCS) sets and propose an iterative process for its solution. Renewed interest in this problem stems from the fact that it was recently discovered to serve…

Given a graded poset $P$, consider a chain decomposition $\mathcal{C}$ of $P$. If $|C_1|\le |C_2|$ implies that the set of the ranks of elements in $C_1$ is a subset of the ranks of elements in $C_2$ for any chains $C_1,C_2\in \mathcal{C}$,…

Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…

The notion of (3+1)-avoidance has shown up in many places in enumerative combinatorics. The natural goal of enumeration of all (3+1)-avoiding posets remains open. In this paper, we enumerate graded (3+1)-avoiding posets for both reasonable…

Many graph problems were first shown to be fixed-parameter tractable using the results of Robertson and Seymour on graph minors. We show that the combination of finite, computable, obstruction sets and efficient order tests is not just one…

In this paper, a new kind of soft sets related with some common decision making problems in real life called central soft sets is introduced. Properties of some basic operations on central soft sets are shown. It is investigated that some…

The non-Abelian exponentiation theorem has recently been generalised to correlators of multiple Wilson line operators. The perturbative expansions of these correlators exponentiate in terms of sets of diagrams called webs, which together…

In this note we introduce the poset of $m$-multichains of a given poset $\mathcal{P}$. Its elements are the multichains of $\mathcal{P}$ consisting of $m$ elements, and its partial order is the componentwise partial order of $\mathcal{P}$.…

We use Sidon sets to present an elementary method to study some combinatorial problems in finite fields, such as sum product estimates, solubility of some equations and distribution of sequences in small intervals. We obtain classic and…

We consider databases in which each attribute takes values from a partially ordered set (poset). This allows one to model a number of interesting scenarios arising in different applications, including quantitative databases, taxonomies, and…

Interpretable part-prototype models are computer vision models that are explainable by design. The models learn prototypical parts and recognise these components in an image, thereby combining classification and explanation. Despite the…

The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain…

We study the problem of checking whether an existential sentence (that is, a first-order sentence in prefix form built using existential quantifiers and all Boolean connectives) is true in a finite partially ordered set (in short, a poset).…

In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…

We study the equivalence relation on the set of acyclic orientations of an undirected graph G generated by source-to-sink conversions. These conversions arise in the contexts of admissible sequences in Coxeter theory, quiver…

This paper is devoted to the online dominating set problem and its variants. We believe the paper represents the first systematic study of the effect of two limitations of online algorithms: making irrevocable decisions while not knowing…

The ideas here are a continuation of a previous article. Some of the applications of the main ideas in the previous article are explained, along with some limitations of the general ideas. There are situations where additional hypotheses…

We examine an elementary problem on prime divisibility of binomial coefficients. Our problem is motivated by several related questions on alternating groups.

Stanley's inequalities for partially ordered sets establish important log-concavity relations for sequences of linear extensions counts. Their extremals however, i.e., the equality cases of these inequalities, were until now poorly…