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The use of techniques from algebra, topology, and geometry in the solution of combinatorial problems, or the use of combinatorial methods to attack problems in these areas ...

The determination of the number of alternating permutations having elements {1,2,...,n}.

An antimagic graph is a graph with e graph edges labeled with distinct elements {1,2,...,e} so that the sum of the graph edge labels at each graph vertex differ.

Araya and Wiener (2011) found the two cubic planar hypohamiltonian graphs on 70 and 88 vertices, respectively, illustrated above.

A directed graph is called an arborescence if, from a given node x known as the root vertex, there is exactly one elementary path from x to every other node y.

The 4-polyhex illustrated above (Gardner 1978, p. 147).

In general, an arrangement of objects is simply a grouping of them. The number of "arrangements" of n items is given either by a combination (order is ignored) or permutation ...

A Sheffer sequence for (1,f(t)) is called the associated sequence for f(t), and a sequence s_n(x) of polynomials satisfying the orthogonality conditions ...

The average disorder number of a simple connected graph on n vertices is defined as the average length of a walk along the edges of the graph taken over all ordering of its ...

A pattern tau=(tau_1,...,tau_n) is said to avoid alpha=(alpha_1,...,alpha_k) if alpha is not contained in tau. In other words, tau avoids alpha iff no k-subset of tau is ...