Twenty-Vertex Entropy Constant

The term twenty-vertex entropy constant is used here for the asymptotic growth constant of Eulerian orientations of the triangular lattice. Let be the lattice graph on an period of the triangular lattice with opposite sides identified, where . Let count its graph orientations in which every graph vertex has three inwardly directed and three outwardly directed edges. These are Eulerian orientations, with possible local configurations at each graph vertex.

Baxter (1969) showed that

			(1)
			(2)
			(3)

(OEIS A104956; Finch 2003, p. 412).

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References

Baxter, R. J. "

Model on a Triangular Lattice." J. Math. Phys. 10, 1211-1216, 1969. https://doi.org/10.1063/1.1664960.Baxter, R. J. Exactly Solved Models in Statistical Mechanics. New York: Academic Press, 1982.Finch, S. R. "Lieb's Square Ice Constant." §5.24 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 412-413, 2003.Sloane, N. J. A. Sequence A104956 in "The On-Line Encyclopedia of Integer Sequences."

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Twenty-Vertex Entropy Constant

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Weisstein, Eric W. "Twenty-Vertex Entropy Constant." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Twenty-VertexEntropyConstant.html

Twenty-Vertex Entropy Constant

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