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The Jack polynomials are a family of multivariate orthogonal polynomials dependent on a positive parameter alpha. Orthogonality of the Jack polynomials is proved in Macdonald ...

The n-dimensional Keller graph, sometimes denoted G_n (e.g., Debroni et al. 2011), can be defined on a vertex set of 4^n elements (m_1,...,m_n) where each m_i is 0, 1, 2, or ...

Consider the plane quartic curve X defined by x^3y+y^3z+z^3x=0, where homogeneous coordinates have been used here so that z can be considered a parameter (the plot above ...

The self-describing sequence consisting of "blocks" of single and double 1s and 2s, where a "block" is a single digit or pair of digits that is different from the digit (or ...

A one-person game played on a rectangular lattice of lamps which can be turned on and off. A move consists of flipping a "switch" inside one of the squares, thereby toggling ...

A Lucas cube graph of order n is a graph that can be defined based on the n-Fibonacci cube graph by forbidding vertex strings that have a 1 both in the first and last ...

A k-matching in a graph G is a set of k edges, no two of which have a vertex in common (i.e., an independent edge set of size k). Let Phi_k be the number of k-matchings in ...

A (k,l)-multigrade equation is a Diophantine equation of the form sum_(i=1)^ln_i^j=sum_(i=1)^lm_i^j (1) for j=1, ..., k, where m and n are l-vectors. Multigrade identities ...

A number n is k-multiperfect (also called a k-multiply perfect number or k-pluperfect number) if sigma(n)=kn for some integer k>2, where sigma(n) is the divisor function. The ...

The natural logarithm of 2 is a transcendental quantity that arises often in decay problems, especially when half-lives are being converted to decay constants. ln2 has ...