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Macdonald's plane partition conjecture proposes a formula for the number of cyclically symmetric plane partitions (CSPPs) of a given integer whose Ferrers diagrams fit inside ...

Circumscribe a triangle about a circle, another circle around the triangle, a square outside the circle, another circle outside the square, and so on. The circumradius and ...

A pair of closed form functions (F,G) is said to be a Wilf-Zeilberger pair if F(n+1,k)-F(n,k)=G(n,k+1)-G(n,k). (1) The Wilf-Zeilberger formalism provides succinct proofs of ...

A q-analog, also called a q-extension or q-generalization, is a mathematical expression parameterized by a quantity q that generalizes a known expression and reduces to the ...

The "15 puzzle" is a sliding square puzzle commonly (but incorrectly) attributed to Sam Loyd. However, research by Slocum and Sonneveld (2006) has revealed that Sam Loyd did ...

A circle is the set of points in a plane that are equidistant from a given point O. The distance r from the center is called the radius, and the point O is called the center. ...

A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all ...

An n-mark Golomb ruler is a set of n distinct nonnegative integers (a_1,a_2,...,a_n), called "marks," such that the positive differences |a_i-a_j|, computed over all possible ...

Analytic number theory is the branch of number theory which uses real and complex analysis to investigate various properties of integers and prime numbers. Examples of topics ...

Let P be the set of primes, and let Q_p and Z_p(t) be the fields of p-adic numbers and formal power series over Z_p=(0,1,...,p-1). Further, suppose that D is a "nonprincipal ...