Hard Hexagon Entropy Constant
N.B. A detailed on-line essay by S. Finchwas the starting point for this entry.
A constant related to the Hard Square Entropy Constant. This constant is given by
 | (1) |
is the number of configurations of nonattacking Kings on an 
chessboard with regular hexagonal cells, where 
. Amazingly, 
is algebraic and given by | (2) |
 |  |  | (3) |
 | |  | (4) |
 | |  | (5) |
 | |  | (6) |
 | |  | (7) |
 | |  | (8) |
 | |  | (9) |
(Baxter 1980, Joyce 1988).
References
Baxter, R. J. ``Hard Hexagons: Exact Solution.'' J. Physics A 13, 1023-1030, 1980. Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/square/square.html Joyce, G. S. ``On the Hard Hexagon Model and the Theory of Modular Functions.'' Phil. Trans. Royal Soc. London A 325, 643-702, 1988. Plouffe, S. ``Hard Hexagons Constant.''http://www.lacim.uqam.ca/piDATA/hardhex.html.
- Hexakaidecagon
- Hexakis Icosahedron
- Hexakis Octahedron
- Hex Game
- Hexlet
- HexLife
- Hex Number
- Hexomino
- Hex (Polyhex)
- Hex Pyramidal Number
- Heyting Algebra
- H-Fractal
- H-Function
- Hh Function
- Higher Arithmetic
- Highest Weight Theorem
- HighLife
- Highly Abundant Number
- Highly Composite Number
- Higman-Sims Group
- Hilbert Basis Theorem
- Hilbert Curve
- Hilbert Function
- Hilbert Hotel
- Hilbert Matrix