33 research outputs found
Enumeration of symmetry classes of convex polyominoes on the honeycomb lattice
Hexagonal polyominoes are polyominoes on the honeycomb lattice. We enumerate
the symmetry classes of convex hexagonal polyominoes. Here convexity is to be
understood as convexity along the three main column directions. We deduce the
generating series of free (i.e. up to reflection and rotation) and of
asymmetric convex hexagonal polyominoes, according to area and half-perimeter.
We give explicit formulas or implicit functional equations for the generating
series, which are convenient for computer algebra.Comment: 21 pages, 16 figures, 2 tables. This is the full version of a paper
presented at the FPSAC Conference in Vancouver, Canada, June 28 -- July 2,
200
Generating functions for generating trees
Certain families of combinatorial objects admit recursive descriptions in
terms of generating trees: each node of the tree corresponds to an object, and
the branch leading to the node encodes the choices made in the construction of
the object. Generating trees lead to a fast computation of enumeration
sequences (sometimes, to explicit formulae as well) and provide efficient
random generation algorithms. We investigate the links between the structural
properties of the rewriting rules defining such trees and the rationality,
algebraicity, or transcendence of the corresponding generating function.Comment: This article corresponds, up to minor typo corrections, to the
article submitted to Discrete Mathematics (Elsevier) in Nov. 1999, and
published in its vol. 246(1-3), March 2002, pp. 29-5
Random Generation Using Binomial Approximations
International audienceGeneralizing an idea used by Alonso to generate uniformly at random Motzkin words, we outline an approach to build efficient random generators using binomial distributions and rejection algorithms. As an application of this method, we present random generators, both efficient and easy to implement, for partial injections and colored unary-binary trees