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Perfect Matchings in Lattice Animals and Lattice Paths with Constraints

Croatian International Relations Review

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Title Perfect Matchings in Lattice Animals and Lattice Paths with Constraints
Savršeno sparivanje kod rešetkastih životinja i rešetkastih putova uz ograničenja
 
Creator Došlić, Tomislav
 
Subject lattice animal; benzenoid graph; polyomino; lattice path; perfect matching; enumeration; Catalan numbers; Schröder numbers; Delannoy numbers
 
Description 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.
U prvom je dijelu članka pokazana uporaba tehnika ušnog rastava u dokazivanju postojanja i izvođenju donjih ocjena broja savršenih sparivanja u benzenoidnim grafovima i poliominima. Nakon toga je uspostavljena korespondencija između savršenih sparivanja u nekim klasama benzenoidnih grafova i putova u pravokutnim rešetkama koji zadovoljavaju određena ograničenja zadana dijagonalama. Korespondencija je zatim rabljena za dobivanje eksplicitnih formula za broj savršenih sparivanja u benzenoidnim grafovima i za izvo|enje identiteta koji uključuju Fibonaccijeve brojeve i binomne koeficijente. Neki od rezultata za benzenoidne grafove su zatim prevedeni u kontekst poliomina.
 
Publisher Croatian Chemical Society
 
Date 2005
 
Type text
info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
 
Format application/pdf
 
Identifier https://hrcak.srce.hr/19
https://hrcak.srce.hr/file/19
 
Source Croatica Chemica Acta
ISSN 0011-1643 (Print)
ISSN 1334-417X (Online)
Volume 78
Issue 2
 
Language eng
 
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