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Enumeriation of parallelogram polyominoes with given bond and site perimeter. (English) Zbl 0651.05027

Summary: We give the generating function for parallelogram polyominoes according to the bond perimeter and the site perimeter. In this last case, we give an asymptotic evaluation for their number. According to the two parameters an exact formula for their number is found which gives some numbers closed to the Narayana’s numbers.

MSC:

05B50 Polyominoes
05A15 Exact enumeration problems, generating functions
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[1] Delest, M.: Generating functions for column-convex polyominoes, Bordeaux Report 8503. J. Comb. Theory (A) (to appear) · Zbl 0736.05030
[2] Delest, M., Viennot, G.: Algebraic languages and polyominoes enumeration. Theor. Comput. Sci.34, 169–206 (1984) · Zbl 0985.68516 · doi:10.1016/0304-3975(84)90116-6
[3] Dhar, D., Phani, M.K., Barma, M.: Enumeration of directed site animals on two-dimensional lattices. J. Phys. A: Math. Gen.15, L279-L284 (1982) · doi:10.1088/0305-4470/15/6/006
[4] Flajolet, P.: Mathematical Analysis of algorithms and data Structures. In: A Graduate Course in Computational Theory. Computer Science Press 1985
[5] Gessel, I., Viennot, G.: Binomial determinants, Paths and Hook lengths formulae. Advances in Math.,36, 300–321 (1986) · Zbl 0579.05004
[6] Golomb, S.: Polyominoes. New York: Scribner 1965
[7] Gouyou-Beauchamps, D.: Deux propriétés du langage de Lukasiewicz, RAIRO, dec.3, 13–24 (1975) · Zbl 0337.05010
[8] Gouyou-Beauchamps, D., Viennot, G.: Equivalence of the two-dimensional directed animal problem. Appl. Maths. (to appear) · Zbl 0727.05036
[9] Klarner, D.: My life among the polyominoes. In: The Mathematical Gardner, pp. 243–262. Belmont CA: Wadsworth 1981 · Zbl 0476.05029
[10] Kreweras, G.: Joint distributions of three descriptive parameters of bridges. In: Colloque de Combinatoire énumérative. Lecture Notes in Mathematics 1234, pp. 177–191. Montréal: UQAM 1985
[11] Narayana, T.V.: A partial order and its applications to probability Theory. Sankhya,21, 91–98 (1959) · Zbl 0168.39202
[12] Polya, G.: On the number of certain lattice polygons. J. Comb. Theoory6, 102–105 (1969) · Zbl 0327.05010 · doi:10.1016/S0021-9800(69)80113-4
[13] Read, R.C.: Contributions to the cell growth problem. Canad. J. Math.14, 1–20 (1962) · Zbl 0105.13510 · doi:10.4153/CJM-1962-001-2
[14] Viennot, G.: Problèmes combinatoires posés par la Physique statistique. Séminaire Bourbaki, 626, Feb. 1984. In: Astérisque, pp. 121–122, 225–246. Soc. Math. France 1985
[15] Viennot, G.: Enumerative combinatorics and algebraic languages. In: Proc. FCT’ 85. Lecture Notes in Computer Science 199, edited by L. Budach, pp. 450–464. Berlin-Heidelberg-New York: Springer 1985 · Zbl 0604.68081
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