The number of convex polyominos with given perimeter
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An elementary proof is given for the number of convex polyominos of perimeter 2 m +4.About:
This article is published in Discrete Mathematics.The article was published on 1988-06-01 and is currently open access. It has received 31 citations till now. The article focuses on the topics: Convex polytope & Elementary proof.read more
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Self-avoiding polygons on the square lattice
Iwan Jensen,Anthony J. Guttmann +1 more
TL;DR: In this paper, an improved algorithm was developed to enumerate the number of self-avoiding polygons on the square lattice to perimeter length 90, where the critical point is indistinguishable from a root of the polynomial 581x4 + 7x2 -13 = 0.500 0005(10).
Journal ArticleDOI
Exact solution of the staircase and row-convex polygon perimeter and area generating function
Richard Brak,Anthony J. Guttmann +1 more
TL;DR: An explicit expression for the perimeter and area generating function G(y, z)= Sigma n>or=2 Sigma m>or =1 cn,mynZm, where cn is the number of row-convex polygons with area m and perimeter n.
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Enumeration of three-dimensional convex polygons
TL;DR: In this article, the authors presented an elementar approach to enumerate convex self-avoiding polygon (SAP) on a graph in any dimension and showed that the generating function for convex SAPs on the cubic lattice is always a quotient of differentiably finite power series.
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Exact solution of the row-convex polygon perimeter generating function
TL;DR: In this paper, an explicit expression for the perimeter generating function G(y)= Sigma n>or=2 any 2n for row-convex polygons on the square lattice, where an is the number of 2n step row-convolutional polygons.
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Generating convex polyominoes at random
TL;DR: A new recursion formula is given for the number of convex polyominoes with fixed perimeter from which a bijection between an interval of natural numbers and the polyminoes of given perimeter is derived, providing a possibility to generate such polyominees at random in polynomial time.
References
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Book
Generalized Hypergeometric Series
TL;DR: Koornwinder as discussed by the authors gave identitity (2.5) with N = 0 and formulas (5.3), 5.3, and 5.4) substituted.
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Binomial Determinants, Paths, and Hook Length Formulae
Ira M. Gessel,Gérard Viennot +1 more
TL;DR: In this paper, a combinatorial interpretation for any minor (or binomial determinant) of the matrix of binomial coefficients is given, involving configurations of nonintersecting paths, and is related to Young tableaux and hook length formulae.
Journal ArticleDOI
Algebraic languages and polyominoes enumeration
TL;DR: It is proved that the number of convex polyominoes with perimeter 2n + 8 is (2n + 11)4 n −4(2 n + 1)( 2n n ) .
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Rigorous results for the number of convex polygons on the square and honeycomb lattices
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