相关论文: Infinite Schnyder Woods

Singularities appear in numerous important mathematical models used in Physics. And in most of such cases singularities are involved in essentially nonlinear contexts. For more than four decades, general enough nonlinear theories of…

We prove polynomial upper and lower bounds on the expected size of the maximum agreement subtree of two random binary phylogenetic trees under both the uniform distribution and Yule-Harding distribution. This positively answers a question…

After a quick review of the representation theory of the symmetric group, we give an exposition of the tools brought about by the so-called half-infinite wedge representation of the infinite symmetric group. We show how these can be applied…

Among other results, we prove the following theorem about Steiner minimal trees in $d$-dimensional Euclidean space: if two finite sets in $\mathbb{R}^d$ have unique and combinatorially equivalent Steiner minimal trees, then there is a…

In this paper, we study ends of complete gradient non-trivial Schouten solitons. Without any additional assumptions, we show the shrinking ones have finitely many ends, and the expanding ones are connected at infinity. We also provide…

We generalise surface cluster algebras to the case of infinite surfaces where the surface contains finitely many accumulation points of boundary marked points. To connect different triangulations of an infinite surface, we consider infinite…

It is shown that a finite monoid can have an infinite irredundant basis of equations.

We show that the Schaeffer's tree for an infinite quadrangulation only changes locally when changing the root of the quadrangulation. This follows from one property of distances in the infinite uniform random quadrangulation.

It is well known that there exist knots with Seifert surfaces of arbitrarily high genus. In this paper, we show the existence of infinitely many knot exteriors where each of which has longitudinal essential surfaces of any positive genus…

In this article we obtain an improved upper bound for the regularity of binomial edge ideals of trees.

A well-known result of Walsh states that if $\mathcal T^*$ is an ideal triangulation of an atoroidal, acylindrical, irreducible, compact 3-manifold with torus boundary components, then every properly embedded, two-sided, incompressible…

We prove the finite-time collapse of a system of N classical fields, which are described by N coupled nonlinear Schrodinger equations. We derive the conditions under which all of the fields experiences this finite-time collapse. Finally,…

Some aspects of a mathematical theory of rigidity and flexibility are developed for general infinite frameworks and two main results are obtained. In the first sufficient conditions, of a uniform local nature, are obtained for the existence…

We show that for every finite set of prime numbers S, there are at most finitely many singular moduli that are S-units. The key new ingredient is that for every prime number p, singular moduli are p-adically disperse. We prove analogous…

We generalize the well-studied notion of a modular pair of a finite matroid to arbitrary families of sets in infinite matroids, and use it to develop the theory of infinite matroids in several as-yet-unexplored areas. Our results include a…

In this paper we study infinitesimal and finite flexibility for generic semidiscrete surfaces. We prove that generic 2-ribbon semidiscrete surfaces have one degree of infinitesimal and finite flexibility. In particular we write down a…

In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schr\"odinger equation in all dimensions based on the recent linear profile decomposition results. We then present a new proof…

We prove that the half plane version of the uniform infinite planar triangulation (UIPT) is recurrent. The key ingredients of the proof are a construction of a new full plane extension of the half plane UIPT, based on a natural…

New estimates on the maximal function associated to the linear Schrodinger equation are established

Starting with the irreducible triangulations of a fixed surface and splitting vertices, all the triangulations of the surface up to a given number of vertices can be generated. The irreducible triangulations have previously been determined…