Polyominoes and Animals: Some Recent Results1
نویسنده
چکیده
We give a survey of recent works relating algebraic languages and formal power series with the enumeration of polyominoes (and animals). More precisely, encoding these structures with words yields new exact results.
منابع مشابه
Polyominoes with Nearly Convex Columns: an Undirected Model
Column-convex polyominoes were introduced in 1950’s by Temperley, a mathematical physicist working on “lattice gases”. By now, column-convex polyominoes are a popular and well-understood model. There exist several generalizations of column-convex polyominoes. However, the enumeration by area has been done for only one of the said generalizations, namely for multi-directed animals. In this paper...
متن کامل0 Statistics of lattice animals ( polyominoes ) and polygons
We have developed an improved algorithm that allows us to enumerate the number of site animals (polyominoes) on the square lattice up to size 46. Analysis of the resulting series yields an improved estimate, τ = 4.062570(8), for the growth constant of lattice animals and confirms to a very high degree of certainty that the generating function has a logarithmic divergence. We prove the bound τ >...
متن کاملA survey of the cell-growth problem and some its variations
A very brief survey of the main results concerning the cell–growth problem and its variations is given. The name stems from an analogy with an animal which, starting from a single cell of some specified basic polygonal shape, grows step by step in the plane by adding at each step a cell of the same shape to its periphery. The fundamental combinatorial problem concerning these animals is ”How ma...
متن کاملOn the Generation and Enumeration of some Classes of Convex Polyominoes
ECO is a method for the recursive generation, and thereby also the enumeration of classes of combinatorial objects. It has already found successful application in recent literature both to the exhaustive generation and to the uniform random generation of various objects classified according to several parameters of interest, as well as to their enumeration. In this paper we extend this approach...
متن کاملThe number of directed k-convex polyominoes
In the plane Z× Z a cell is a unit square and a polyomino is a finite connected union of cells. Polyominoes are defined up to translations. Since they have been introduced by Golomb [20], polyominoes have become quite popular combinatorial objects and have shown relations with many mathematical problems, such as tilings [6], or games [19] among many others. Two of the most relevant combinatoria...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004