Asymptotic bounds for the number of convex \(n\)-ominoes

DOI10.1016/0012-365X(74)90107-1zbMath0274.05111OpenAlexW2070622420MaRDI QIDQ2264682

Ronald L. Rivest, David A. Klarner

Publication date: 1974

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0012-365x(74)90107-1

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Enumeration in graph theory (05C30) Other designs, configurations (05B30) Linear integral equations (45A05)

Related Items (22)

Combinatorial objects enumerated by \(q\)-Bessel functions ⋮ The generating function of convex polyominoes: The resolution of a \(q\)- differential system ⋮ Algebraic languages and polyominoes enumeration ⋮ Part Sizes of Smooth Supercritical Compositional Structures ⋮ On the enumeration of \(k\)-omino towers ⋮ A method for the enumeration of various classes of column-convex polygons ⋮ Enumeration of the directed convex polyominoes ⋮ On the area of square lattice polygons. ⋮ GENERATING FUNCTIONS FOR THE NUMBERS OF PYRAMID AND STAIRCASE POLYHEDRA ⋮ Concatenation arguments and their applications to polyominoes and polycubes ⋮ Empilements de segments et \(q\)-énumération de polyominos convexes dirigés. (Heaps of segments and \(q\)-enumeration of directed convex polyominoes) ⋮ Families of \(m\)-convex polygons: \(m=1\) ⋮ The average height of directed column-convex polyominoes having square, hexagonal and triangular cells ⋮ Symmetric peaks and symmetric valleys in Dyck paths ⋮ Unnamed Item ⋮ Length enumeration of fully commutative elements in finite and affine Coxeter groups ⋮ Generating functions for column-convex polyominoes ⋮ Enumeration of symmetry classes of convex polyominoes in the square lattice ⋮ Exactly Solved Models ⋮ Steep polyominoes, \(q\)-Motzkin numbers and \(q\)-Bessel functions ⋮ Convex n-ominoes ⋮ \(q\)-enumeration of convex polyominoes

Cites Work

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• Contributions to the Cell Growth Problem
• On the number of certain lattice polygons
• A combinatorial formula involving the Fredholm integral equation
• Cell Growth Problems
• STACKS
• A Procedure for Improving the Upper Bound for the Number of n-Ominoes

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