Binary Binary numeral system The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...	1.10001010001000110100010111001100…
Decimal Decimal The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....	1.539600717839002…
Hexadecimal Hexadecimal In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen...	1.8A2345CC0442…
Continued fraction Continued fraction In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on...

Lieb's square ice constant is a mathematical constant

Mathematical constant

A mathematical constant is a special number, usually a real number, that is "significantly interesting in some way". Constants arise in many different areas of mathematics, with constants such as and occurring in such diverse contexts as geometry, number theory and calculus.What it means for a...

 used in the field of combinatorics

Combinatorics

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...

. It was introduced by Elliott H. Lieb

Elliott H. Lieb

Elliott H. Lieb is an eminent American mathematical physicist and professor of mathematics and physics at Princeton University who specializes in statistical mechanics, condensed matter theory, and functional analysis....

 in 1967.

Definition

Let L denote the area of an n × n square lattice

Square lattice

In mathematics, the square lattice is a type of lattice in a two-dimensional Euclidean space. It is the two-dimensional version of the integer lattice. It is one of the five types of two-dimensional lattices as classified by their symmetry groups; its symmetry group is known symbolically as p4m.Two...

, where L = n². Assign a direction to each edge of the lattice. Denote the number of orientations of such that each vertex

Vertex (geometry)

In geometry, a vertex is a special kind of point that describes the corners or intersections of geometric shapes.-Of an angle:...

 has two inwardly directed and two outwardly directed edges by f(n).

Some historical and physical background can be found in the article Ice-type model

Ice-type model

In statistical mechanics, the ice-type models or six-vertex models are a family of vertex models for crystal lattices with hydrogen bonds. The first such model was introduced by Linus Pauling in 1935 to account for the residual entropy of water ice. Variants have been proposed as models of certain...

.