In this report we review the literature in the area of combinatorial enumeration in chemistry published in the last two years – from June 2001 to May 2003. In our earlier report we presented historically important isomer enumerations,

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The design of an object-oriented framework for combinatorial enumeration is described. Combinatorial enumeration requires a subtle interplay between the search mechanism, the ordering of the space of combinatorial objects, and the symmetries used to prune equivalent cases from the search

This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and hypergraphs, relational structures, and others. The second part

of the anonymity provided by the system. Here we extend this approach to include in the calculation information about how many messages were sent or received by a user and we define a new metric that can be computed exactly and efficiently using classical and elegant techniques from combinatorial enumeration. 1

and the algorithmCombinatorial enumeration ◮ Example of problem considered: ◮ List all 3-valent plane graphs with faces of gonality 5 and 9 and all 9-gonal faces in pairs. ◮ List all independent sets of 600-cell. ◮ List all triangulations of the sphere on n vertices. ◮ List all isohedral (r, q

The aim of these lectures was to give an overview of some combinatorial, symmetricfunction theoretic, and representation-theoretic developments during the last several years in the theory of Hall-Littlewood and Macdonald polynomials. The motivating problem for all these developments was Macdonald’s

Abstract. Given a complete graph with positive weights on its edges, we define the weight of a subset of edges as the product of weights of the edges in the subset and consider sums (partition functions) of weights over subsets of various kinds: cycle covers, closed walks, spanning trees. We show that if the weights of the edges of the graph are within a constant factor, fixed in advance, of each other then the bulk of the partition function is concentrated on the subsets of a particularly simple structure: cycle covers with few cycles, walks that visit every vertex only few times, and spanning trees with small degree of every vertex. This allows us to construct a polynomial time algorithm to separate graphs with many Hamiltonian cycles from graphs that are sufficiently far from Hamiltonian. 1. Introduction and

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In this paper systems of functional equations in infinitely many variables arising in combinatorial enumeration problems are studied. We prove sufficient conditions under which the combinatorial random variables encoded in the generating functions of the system tend to an infinite dimensional