Lieb's square ice constant

Lieb's square ice constant

Lieb's square ice constant is a mathematical constant used in the field of combinatorics. It was introduced by Elliott H. Lieb in 1967. [cite web|url=http://prola.aps.org/abstract/PR/v162/i1/p162_1|title=Phys. Rev. 162, 162 - 172 (1967)|accessdate=2008-03-18]

Definition

Let "L" denote the area of an "n" × "n" square lattice, where "L" = "n"2 Assign a direction to each edge of the lattice. Denote the number of orientations of such that each vertex has two inwardly directed and two outwardly directled edges by ƒ("n").

: lim_{n o infty}(f(n))^{n^{-2=left(frac{4}{3} ight)^frac{3}{2}=frac{8 sqrt{3{9}=1.5396007dots

References


Wikimedia Foundation. 2010.

Игры ⚽ Нужна курсовая?

Look at other dictionaries:

  • Mathematical constant — A mathematical constant is a special number, usually a real number, that is significantly interesting in some way .[1] Constants arise in many different areas of mathematics, with constants such as e and π occurring in such diverse contexts as… …   Wikipedia

  • List of mathematics articles (L) — NOTOC L L (complexity) L BFGS L² cohomology L function L game L notation L system L theory L Analyse des Infiniment Petits pour l Intelligence des Lignes Courbes L Hôpital s rule L(R) La Géométrie Labeled graph Labelled enumeration theorem Lack… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”