Related papers: On the Queue-Number of Partial Orders
A cutset is a non-empty finite subset of $\mathbb{Z}^d$ which is both connected and co-connected. A cutset is odd if its vertex boundary lies in the odd bipartition class of $\mathbb{Z}^d$. Peled suggested that the number of odd cutsets…
Unit-generated orders of a quadratic field are orders of the form $\mathcal{O} = \mathbb{Z}[\varepsilon]$, where $\varepsilon$ is a unit in the quadratic field. If the order $\mathcal{O}$ is a maximal order of a real quadratic field, then…
A \emph{$(k,t)$-track layout} of a graph $G$ consists of a (proper) vertex $t$-colouring of $G$, a total order of each vertex colour class, and a (non-proper) edge $k$-colouring such that between each pair of colour classes no two…
Cobweb posets uniquely represented by directed acyclic graphs are such a generalization of the Fibonacci tree that allows joint combinatorial interpretation for all of them under admissibility condition. This interpretation was derived in…
A $k$-stack layout (or $k$-page book embedding) of a graph consists of a total order of the vertices, and a partition of the edges into $k$ sets of non-crossing edges with respect to the vertex order. The stack number of a graph is the…
In this paper we give an algorithm to determine, for any given suborder closed class of series-parallel posets, a structure theorem for the class. We refer to these structure theorems as structural descriptions.
The W-set of an element of a weak order poset is useful in the cohomological study of the closures of spherical subgroups in generalized flag varieties. We explicitly describe in a purely combinatorial manner the W-sets of the weak order…
The $1/3$-$2/3$ Conjecture, originally formulated in 1968, is one of the best-known open problems in the theory of posets, stating that the balance constant (a quantity determined by the linear extensions) of any non-total order is at least…
Given a straight-line drawing of a graph, a segment is a maximal set of edges that form a line segment. Given a planar graph $G$, the segment number of $G$ is the minimum number of segments that can be achieved by any planar straight-line…
The order and chain polytopes, introduced by Richard P. Stanley, form a pair of Ehrhart equivalent polytopes associated to a given finite poset. A conjecture by Takayuki Hibi and Nan Li states that the $f$-vector of the chain polytope…
S. Gudder and, later, S. Pulmanova and E. Vincekova, have studied in two recent papers a certain ordering of bounded self-adjoint operators on a Hilbert space. We present some further results on this ordering and show that some structure…
Paraorthomodular posets are bounded partially ordered set with an antitone involution induced by quantum structures arising from the logico-algebraic approach to quantum mechanics. The aim of the present work is starting a systematic…
We introduce and study additive posets. We show that the top homology group (with coefficients in Z/2Z) of a finite dimensional CW-complex carries a structure of an additive poset invariant under subdivisions. Applications to CW-complexes…
The paper examines a partial order on bipartite graphs (X1, X2, E) with n vertices, X1UX2={1,2,...,n}. This partial order is a natural partial order of subobjects of an object in a triangular category with bipartite graphs as morphisms.
We present a matrix-theoretic approach for studying and enumerating finite posets through their incidence representations, referred to as poset matrices. Naturally labelled posets are encoded as Boolean lower triangular matrices, allowing a…
Dujmovi\'{c}, Joret, Micek, Morin, Ueckerdt and Wood recently in [Planar graphs have bounded queue-number, Journal of the ACM, Volume 67, Issue 4, Article No.: 22, August 2020] showed some attractive graph product structure theorems for…
This paper considers a population process on a dynamically evolving graph, which can be alternatively interpreted as a queueing network. The queues are of infinite-server type, entailing that at each node all customers present are served in…
A combinatorial study of multiple $q$-integrals is developed. This includes a $q$-volume of a convex polytope, which depends upon the order of $q$-integration. A multiple $q$-integral over an order polytope of a poset is interpreted as a…
We study subclasses of grid intersection graphs from the perspective of order dimension. We show that partial orders of height two whose comparability graph is a grid intersection graph have order dimension at most four. Starting from this…
The elements of a finite nonempty partially ordered set are exposed at independent uniform times in $[0,1]$ to a selector who, at any given time, can see the structure of the induced partial order on the exposed elements. The selector's…