On Appel Index of MATH/CHEM/COMP Conference

An index measuring the mathematical content of an interdisciplinary area is described and calculated for the MATH/CHEM/COMP conference. Some further areas of application of this index in mathematical chemistry are indicated

Savršeno sparivanje kod rešetkastih životinja i rešetkastih putova uz ograničenja

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

Tilings of a honeycomb strip and higher order Fibonacci numbers

In this paper we explore two types of tilings of a honeycomb strip and derive some closed form formulas for the number of tilings. Furthermore, we obtain some new identities involving tribonacci numbers, Padovan numbers and Narayana's cow sequence and provide combinatorial proofs for several known identities about those numbers

Importance and Redundancy in Fullerene Graphs

The concept of importance of an edge in a fullerene graph has been defined and lower bounds have been established for this quantity. These lower bounds are then used to obtain an improved lower bound on the number of perfect matchings in fullerene graphs

Morgan Trees and Dyck Paths

A simple bijection is established between Morgan trees and Dyck paths. As a consequence, exact enumerative results for Morgan trees on given number of vertices are obtained in terms of Catalan numbers. The results are further refined by enumerating all Morgan trees with prescribed number of internal vertices and by computing the average number of internal vertices in a Morgan tree

Enumerative aspects of secondary structures

AbstractA secondary structure is a planar, labeled graph on the vertex set {1,…,n} having two kind of edges: the segments [i,i+1], for 1⩽i⩽n−1 and arcs in the upper half-plane connecting some vertices i,j, i⩽j, where j−i>l, for some fixed integer l. Any two arcs must be totally disjoint. We enumerate secondary structures with respect to their size n, rank l and order k (number of arcs), obtaining recursions and, in some cases, explicit formulae in terms of Motzkin, Catalan, and Narayana numbers. We give the asymptotics for the enumerating sequences and prove their log-convexity, log-concavity and unimodality. It is shown how these structures are connected with hypergeometric functions and orthogonal polynomials