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The snub cubical graph is the Archimedean graph on 24 nodes and 60 edges obtained by taking the skeleton of the snub cube. It is a quintic graph, is planar, Hamiltonian, and ...

A symmetric polynomial on n variables x_1, ..., x_n (also called a totally symmetric polynomial) is a function that is unchanged by any permutation of its variables. In other ...

One form of van der Waerden's theorem states that for all positive integers k and r, there exists a constant n(r,k) such that if n_0>=n(r,k) and {1,2,...,n_0} subset C_1 ...

There are three types of cubic lattices corresponding to three types of cubic close packing, as summarized in the following table. Now that the Kepler conjecture has been ...

Assume that n numbered pancakes are stacked, and that a spatula can be used to reverse the order of the top k pancakes for 2<=k<=n. Then the pancake sorting problem asks how ...

Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions. In common ...

Tutte's fragment (Taylor 1997) is the 15-node graph illustrated above (Grünbaum 2003, pp. 358-359 and Fig. 17.1.3). If the graph obtained by adding pendant edges to corners ...

"The" tetrahedral graph is the Platonic graph that is the unique polyhedral graph on four nodes which is also the complete graph K_4 and therefore also the wheel graph W_4. ...

P(n), sometimes also denoted p(n) (Abramowitz and Stegun 1972, p. 825; Comtet 1974, p. 94; Hardy and Wright 1979, p. 273; Conway and Guy 1996, p. 94; Andrews 1998, p. 1), ...