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Abstract: We list several open problems concerning the enumeration of directed animals on two-dimensional lattices. We show that most of these problems are special cases of two central problems: calculating the position generating function and the perimeter and area generating function for square lattice animals. We propose a possible direction for solving these two problems: we extend Dhar's correspondence between hard particle gas models and enumeration of animals according to the area, and show that... (Update)
Context of citations to this paper: More
...to be 9 11. There exist two main approaches to solve directed animals problems: equivalences with hard particle models [1, 2, 3, 4] and purely combinatorial approaches: bijections with one dimensional paths [5] and heaps of pieces [6, 7, 8] Bousquet M elou and Conway...
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BibTeX entry: (Update)
M. Bousquet-M'elou. New enumerative results on two-dimensional directed animals. Discrete Math., 180:73--106, 1998. http://citeseer.ist.psu.edu/568967.html More
@misc{ bousquet-m'elou98new,
author = "M. Bousquet-M'elou",
title = "New enumerative results on two-dimensional directed animals",
text = "M. Bousquet-M'elou. New enumerative results on two-dimensional directed
animals. Discrete Math., 180:73--106, 1998.",
year = "1998",
url = "citeseer.ist.psu.edu/568967.html" }
Citations (may not include all citations):168 Non-negative matrices and Markov chains (context) - Seneta - 1981
160 Exactly solved models in statistical mechanics (context) - Baxter - 1982
74 Introduction to percolation theory (context) - Stauffer, Aharony - 1992
12 Equivalence of the two-dimensional directed site animal prob.. (context) - Dhar - 1983
11 Heaps of pieces I: Basic definitions and combinatorial lemma.. (context) - Viennot - 1986
10 Equivalence of the two-dimensional directed animal problem t.. (context) - Gouyou-Beauchamps, Viennot - 1988
9 Exact solution of a directed-site animals-enumeration proble.. (context) - Dhar - 1983
8 A procedure for improving the upper bound for the number of .. (context) - Klarner, Rivest - 1973
6 Champs al'eatoires sur un r'eseau (context) - Guyon - 1993
6 Directed lattice animals in 2 dimensions: numerical and exac.. (context) - Nadal, Derrida et al. - 1982
6 Enumeration of directed site animals on two-dimensional latt.. (context) - Dhar, Phani et al. - 1982
5 Enumeration of directed site animals on the decorated square.. (context) - Ali - 1994
5 Directed animals on two-dimensional lattices (context) - Conway, Brak et al. - 1993
4 the solvability of some statistical mechanical systems (context) - Guttmann, Enting
4 Some exact results for moments of 2D directed animals (context) - Conway - 1995
3 Animaux et arbres guingois (context) - B'etr'ema, Penaud - 1993
3 Polyominos et pavages (context) - Denise, Penaud et al. - 1992
3 the behaviour of self-avoiding walks and related problems (context) - Conway - 1993
3 Series expansions for directed bond-percolation problem (context) - Blease - 1977
3 eles avec particules dures, animaux dirig (context) - B'etr'ema, Penaud - 1993
2 To be published in Europ (context) - Bousquet-M'elou, models et al. - 1995
2 the number of lattice animals embeddable in the square latti.. (context) - Guttmann - 1982
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