相关论文: Counting Hexagonal Lattice Animals
Lattice animals provide a discretized model for the theta transition displayed by branched polymers in solvent. Exact graph enumeration studies have given some indications that the phase diagram of such lattice animals may contain two…
In this paper, we revisit the enumeration of directed animals using gas models. We show that there exists a natural construction of random directed animals on any directed graph together with a particle system that explains at the level of…
We show that for almost every translation surface the number of pairs of saddle connections with bounded magnitude of the cross product has asymptotic growth like $c R^2$ where the constant $c$ depends only on the area and the connected…
An important problem in analytic and geometric combinatorics is estimating the number of lattice points in a compact convex set in a Euclidean space. Such estimates have numerous applications throughout mathematics. In this note, we exhibit…
In this paper, we present our ongoing work and initial results on the formal specification and verification of MiniMaple (a substantial subset of Maple with slight extensions) programs. The main goal of our work is to find behavioral errors…
We show how to translate the task of computing the multiplicative structure of a Chow ring of a projective homogeneous variety into an easily understandable combinatorial task of calculating in the corresponding polynomial ring. The…
This note wants to explain how to obtain meaningful pictures of (possibly high-dimensional) convex polytopes, triangulated manifolds, and other objects from the realm of geometric combinatorics such as tight spans of finite metric spaces…
We present a novel approach for data set scaling based on scale-measures from formal concept analysis, i.e., continuous maps between closure systems, and derive a canonical representation. Moreover, we prove said scale-measures are lattice…
This paper describes the RationalMaps package for Macaulay2. This package provides functionality for computing several aspects of rational maps such as whether a map is birational, or a closed embedding.
In the last decade major steps towards an algorithmic treatment of orthogonal polynomials and special functions (OP & SF) have been made, notably Zeilberger's brilliant extension of Gosper's algorithm on algorithmic definite hypergeometric…
Let $G$ be a semisimple algebraic group. We develop a machinery for manipulation and manufacture of well-rounded families $\left\{ \mathcal{B}_{T}\right\} _{T>0}\subset G$ as they were defined in a work by A. Gorodnik and A. Nevo. The…
We introduce the arithmetic width of a convex body, defined as the number of distinct values a linear functional attains on the lattice points within the body. Arithmetic width refines lattice width by detecting gaps in the lattice point…
We provide a "soft" proof for non-trivial bounds on spherical, hyperbolic and unipotent Fourier coefficients of a fixed Maass form for a general co-finite lattice $\Gamma$ in $PGL(2,R)$. We use the amplification method based on the Airy…
We report on a package of routines for the computer algebra system Maple which supports the explicit determination of the geometric quantities, field equations, equations of motion, and conserved quantities of General Relativity in the…
The technique of guessing can be very fruitful when dealing with sequences which arise in practice. This holds true especially when guessing is performed algorithmically and efficiently. One highly useful tool for this purpose is the…
The image of a polynomial map is a constructible set. While computing its closure is standard in computer algebra systems, a procedure for computing the constructible set itself is not. We provide a new algorithm, based on algebro-geometric…
We calculate the number of open walks of fixed length and algebraic area on a square planar lattice by an extension of the operator method used for the enumeration of closed walks. The open walk area is defined by closing the walks with a…
A method of embedding partially ordered sets into linear spaces is presented. The problem of finding all orthocomplementations in a finite lattice is reduced to a linear programming problem.
Lattice Green functions appear in lattice gauge theories, in lattice models of statistical physics and in random walks. Here, space coordinates are treated as parameters and series expansions in the mass are obtained. The singular points in…
A symbolic-computational algorithm, fully implemented in Maple, is described, that computes explicit expressions for generating functions that enable the efficient computations of the expectation, variance, and higher moments, of the random…