Croatica Chemica Acta, Vol. 78 No. 2, 2005.
Izvorni znanstveni članak
Perfect Matchings in Lattice Animals and Lattice Paths with Constraints
Tomislav Došlić
Sažetak
In the first part of this paper it is shown how to use ear decomposition techniques in proving existence and establishing lower bounds to the number of perfect matchings in lattice animals. A correspondence is then established between perfect matchings in certain classes of benzenoid graphs and paths in the rectangular lattice that satisfy certain diagonal constraints. This correspondence is used to give explicit formulas for the number of perfect matchings in hexagonal benzenoid graphs and to derive some identities involving Fibonacci numbers and binomial coefficients. Some of the results about benzenoid graphs are also translated into the context of polyominoes.
Ključne riječi
lattice animal; benzenoid graph; polyomino; lattice path; perfect matching; enumeration; Catalan numbers; Schröder numbers; Delannoy numbers
Hrčak ID:
19
URI
Datum izdavanja:
15.6.2005.
Posjeta: 3.128 *