相关论文: Navigating Posets with Few Maps
In this paper, we study two classic optimization problems: minimum geometric dominating set and set cover. In the dominating-set problem, for a given set of objects in {the} plane as input, the objective is to choose a minimum number of…
Let $\mathfrak{P}_r$ be a representation system of the non-isomorphic finite posets, and let ${\cal H}(P,Q)$ be the set of order homomorphisms from $P$ to $Q$. For finite posets $R$ and $S$, we write $R \sqsubseteq_G S$ iff, for every $P…
A linear extension of a poset $P$ is a permutation of the elements of the set that respects the partial order. Let $L(P)$ denote the number of linear extensions. It is a #P complete problem to determine $L(P)$ exactly for an arbitrary…
A plane poset is a finite set with two partial orders, satisfying a certain incompatibility condition. The set PP of isoclasses of plane posets owns two products, and an infinitesimal Hopf algebra structure is defined on the vector space…
For a finite set of integers such that the first few gaps between its consecutive elements equal $a$, while the remaining gaps equal $b$, we study dense packings of its translates on the line. We obtain an explicit lower bound on the…
Let $P$ be a finite poset of width two, i.e., with no three-element antichain. We associate with $P$ a skew Young diagram $\Upsilon(P)$ and discuss some of the properties of the map $\Upsilon$. In particular, if we regard $\Upsilon(P)$ as a…
In this paper, we study the posets of classes of subgroups of finite group having same set of orders of elements. We show that this poset is a chain only in the case of p-groups and moreover, we characterize all finite groups for which this…
For a finite non-empty set $X$, let $\mathfrak{P}(X)$ denote the set of all posets with carrier $X$, ordered by inclusion of their partial order relations. We investigate properties of posets $P \in \mathfrak{P}(X)$ for which no lower cover…
We describe small dominating sets of the incidence graphs of finite projective planes by establishing a stability result which shows that dominating sets are strongly related to blocking and covering sets. Our main result states that if a…
Given a dominating set, how much smaller a dominating set can we find through elementary operations? Here, we proceed by iterative vertex addition and removal while maintaining the property that the set forms a dominating set of bounded…
For $P$ a poset, the dimension of $P$ is defined to be the least cardinal $\kappa$ such that $P$ is embeddable in a direct product of $\kappa$ totally ordered sets. We study the behavior of this function on finite-dimensional (not…
It is well known that every stable matching instance $I$ has a rotation poset $R(I)$ that can be computed efficiently and the downsets of $R(I)$ are in one-to-one correspondence with the stable matchings of $I$. Furthermore, for every poset…
We discuss a possible characterization, by means of forbidden configurations, of posets which are embeddable in a product of finitely many scattered chains.
The goal of this paper is to prove that several variants of deciding whether a poset can be (weakly) embedded into a small Boolean lattice, or to a few consecutive levels of a Boolean lattice, are NP-complete, answering a question of Griggs…
Density of stable maps is the common thread of this paper. We review Whitney's contribution to singularities of differentiable mappings and Thom-Mather theories on $C^{\infty}$ and $C^{0}$-stability. Infinitesimal and algebraic methods are…
In this article we introduce the $m$-cover poset of an arbitrary bounded poset $\mathcal{P}$, which is a certain subposet of the $m$-fold direct product of $\mathcal{P}$ with itself. Its ground set consists of multichains of $\mathcal{P}$…
A poset is a containment of paths in a tree (CPT) if it admits a representation by containment where each element of the poset is represented by a path in a tree and two elements are comparable in the poset if and only if the corresponding…
For any finite poset $P$ we have the poset of isotone maps $\text{Hom}(P,\mathbb{N})$, also called $P^{op}$-partitions. To any poset ideal ${\mathcal J}$ in $\text{Hom}(P,\mathbb{N})$, finite or infinite, we associate monomial ideals: the…
A poset $\mathbf{P} = (X,\preceq)$ is {\em $m$-partite} if $X$ has a partition $X = X_1 \cup ... \cup X_m$ such that (1) each $X_i$ forms an antichain in $\mathbf{P}$, and (2) $x\prec y$ implies $x\in X_i$ and $y\in X_j$ where $i<j$. In…
We study the partial orderings of the form $\langle {\mathbb P} ({\mathbb X}), \subset \rangle $, where ${\mathbb X}$ is a binary relational structure with the connectivity components isomorphic to a strongly connected structure ${\mathbb…