The three dimensional polyominoes of minimal area

Electronic Journal of Combinatorics

Volumn 3, Issue 1 R, 1996, Pages 1-39

  Alonso, Laurent ^a   Cerf, Raphaël ^b  

^a LORIA   (France)

^b CNRS   (France)

Author keywords

Ising model; Isoperimetry; Minimal area; Polyominoes

Indexed keywords

EID: 0041543083     PISSN: 10778926     EISSN: 10778926     Source Type: Journal    
DOI: 10.37236/1251     Document Type: Article

References (11)

1. G.E. Andrews, The theory of partitions, Encyclopedia of Mathematics and its Applications, Addison-Wesley, 1976.
2. G. Ben Arous and R. Cerf, Metastability of the three dimensional Ising model on a torus at very low temperatures, Electronic Journal of Probability 1 (1996), 1-55.
3. B. Bollobás and I. Leader, Compressions and isoperimetric inequalities, J. Combinatorial Theory Series A 56 (1991), 47-62.
4. M. Bousquet-Mélou and J.M. Fédou, The generating function of convex polyominoes: the resolution of a q-differential system, Discrete Math. 137 (1995), 53-75.
5. O. Catoni and R. Cerf, The exit path of a Markov chain with rare transitions, ESAIM: Probabilités et Statistique (1996) (to appear).
6. M.-P. Delest and G. Viennot, Algebraic languages and polyominoes enumeration, Theoret. Comput. Sci. 34 (1984), 169-206.
7. M.I. Freidlin and A.D. Wentzell, Random perturbations of dynamical systems, Springer-Verlag, New York, 1984.
8. E.J. Neves, A discrete variational problem related to Ising droplets at low temperatures, Jour. Stat. Phys. 80 nos 1/2 (1995), 103-123.
9. E.J. Neves and R.H. Schonmann, Critical droplets and metastability for a Glauber dynamics at very low temperatures, Commun. Math. Phys. 137 (1991), 209-230.
10. E. J. Neves and R.H. Schonmann, Behaviour of droplets for a class of Glauber dynamics at very low temperatures, Prob. Th. Related Fields 91 (1992), 331-354.
11. R.H. Schonmann, The pattern of escape from metastability of a stochastic Ising model, Commun. Math. Phys 147 (1992), 231-240.