G S Joyce 1989 J. Phys. A: Math. Gen. 22 L919 doi:10.1088/0305-4470/22/19/001
On the Dhar directed-site animals-enumeration problem for the simple cubic lattice
G S Joyce
Show affiliationsIt is proved that the generating function A(y) for the Dhar directed-site animals-enumeration problem on the simple cubic lattice is an algebraic function. This results is used to analyse the detailed critical behaviour of A(y) as y to yc-, where yc=1/22(-9+5 square root 5). Next an asymptotic expansion for the total number An of directed lattice animals with n sites is derived. Finally, an exact closed-form expression for the generating function A(y) is given.
- PACS
- MSC
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41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (See also 30E15)
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
- Subjects
- Dates
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Issue 19 (7 October 1989)
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On the Dhar directed-site animals-enumeration problem for the simple cubic lattice
G S Joyce 1989 J. Phys. A: Math. Gen. 22 L919
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