Related papers: Counting linear extensions of restricted posets

We prove that for any partition of a set which contains an infinite arithmetic (respectively geometric) progression into two disjoint subsets, at least one of these subsets contains an infinite number of triplets such that each triplet is…

Consider a plane graph G, drawn with straight lines. For every pair a,b of vertices of G, we compare the shortest-path distance between a and b in G (with Euclidean edge lengths) to their actual distance in the plane. The worst-case ratio…

The complexity of the graph isomorphism problem for trapezoid graphs has been open over a decade. This paper shows that the problem is GI-complete. More precisely, we show that the graph isomorphism problem is GI-complete for comparability…

Proper classes of extensions of real field was defined and topological properties of these extensions were studied. These extensions can be connected, in this case such set is not closed under binary operations (addition and…

We investigate connected posets $C$ of height one as retracts of finite posets $P$. We define two multigraphs: a multigraph $\mathfrak{F}(P)$ reflecting the network of so-called improper 4-crown bundles contained in the extremal points of…

This paper presents combinatorial facts dealing with the number of unlabeled partially ordered sets (posets) refined by the number of arcs in the Hasse diagram (sequence A342447 in OEIS). The main result is that the differences with respect…

In order to calculate the multiplicity of an isolated rational curve C in a local complete intersection variety X, i.e. the length of the Hilbert scheme of X at [C], it is important to study infinitesimal neighborhoods of the curve in X.…

In this paper, we propose new lower and upper bounds on the linear extension complexity of regular $n$-gons. Our bounds are based on the equivalence between the computation of (i) an extended formulation of size $r$ of a polytope $P$, and…

We consider the problem of stretching pseudolines in a planar straight-line drawing to straight lines while preserving the straightness and the combinatorial embedding of the drawing. We answer open questions by Mchedlidze et al. by showing…

We prove that any self-contracted curve in R 2 endowed with a C 2 and strictly convex norm, has finite length. The proof follows from the study of the curve bisector of two points in R 2 for a general norm together with an adaptation of the…

We enumerate the connected graphs that contain a linear number of edges with respect to the number of vertices. So far, only the first term of the asymptotics was known. Using analytic combinatorics, i.e. generating function manipulations,…

Let $G$ be a finite group and let $H_1,H_2<G$ be two subgroups. In this paper, we are concerned with the bipartite graph whose vertices are $G/H_1\cup G/H_2$ and a coset $g_1H_1$ is connected with another coset $g_2H_2$ if and only if…

We give a combinatorial upper bound for the gonality of a curve that is defined by a bivariate Laurent polynomial with given Newton polygon. We conjecture that this bound is generically attained, and provide proofs in a considerable number…

In this paper, we show that any finite simplicial complex is homeomorphic to the inverse limit of a sequence of finite posets, which is an extension of Claders result.

This paper is a contribution to the study of extensions of arbitrary models of ZF (Zermelo-Fraenkel set theory), with no regard to countability or well-foundedness of the models involved. We present some new constructions of certain types…

It is elementary and well-known that if an element x of a bounded modular lattice L has a complement in L then x has a relative complement in every interval [a,b] containing x. We show that the relatively strong assumption of modularity of…

For a fairly general class of two-dimensional tiling substitutions, we prove that if the length expansion $\beta$ is a Pisot number, then the tilings defined by the substitution must be locally finite. We also give a simple example of a…

We present bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (2+2)-free posets and a certain class of involutions (or chord diagrams), already appeared in the literature, but were apparently not…

We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.

We establish bounds on a finite separable extension of function fields in terms of the relative class number, thus reducing the problem of classifying extensions with a fixed relative class number to a finite computation. We also solve the…