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A riffle shuffle, in which the top half of the deck is placed in the left hand, and cards are then alternatively interleaved from the left and right hands. Using an ...

The nth central binomial coefficient is defined as (2n; n) = ((2n)!)/((n!)^2) (1) = (2^n(2n-1)!!)/(n!), (2) where (n; k) is a binomial coefficient, n! is a factorial, and n!! ...

The fraction of odd values of the partition function P(n) is roughly 50%, independent of n, whereas odd values of Q(n) occur with ever decreasing frequency as n becomes ...

Consider a collection of diagonal matrices H_1,...,H_k, which span a subspace h. Then the ith eigenvalue, i.e., the ith entry along the diagonal, is a linear functional on h, ...

The mean deviation (also called the mean absolute deviation) is the mean of the absolute deviations of a set of data about the data's mean. For a sample size N, the mean ...

A cubic vertex-transitive graph is a cubic graph that is vertex transitive. Read and Wilson (1998, pp. 161-163) enumerate all connected cubic vertex-transitive graphs on 34 ...

The recursive sequence generated by the recurrence equation Q(n)=Q(n-Q(n-1))+Q(n-Q(n-2)), with Q(1)=Q(2)=1. The first few values are 1, 1, 2, 3, 3, 4, 5, 5, 6, 6, ... (OEIS ...

The regular hexagon is the regular polygon with six sides, as illustrated above. The inradius r, circumradius R, sagitta s, and area A of a regular hexagon can be computed ...

"The" octahedral graph is the 6-node 12-edge Platonic graph having the connectivity of the octahedron. It is isomorphic to the circulant graph Ci_6(1,2), the cocktail party ...

The small dodecahemicosahedron is the uniform polyhedron with Maeder index 62 (Maeder 1997), Wenninger index 100 (Wenninger 1989), Coxeter index 78 (Coxeter et al. 1954), and ...