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The q-analog of integration is given by int_0^1f(x)d(q,x)=(1-q)sum_(i=0)^inftyf(q^i)q^i, (1) which reduces to int_0^1f(x)dx (2) in the case q->1^- (Andrews 1986 p. 10). ...

A Heronian triangle is a triangle having rational side lengths and rational area. The triangles are so named because such triangles are related to Heron's formula ...

The Kneser graphs are a class of graph introduced by Lovász (1978) to prove Kneser's conjecture. Given two positive integers n and k, the Kneser graph K(n,k), often denoted ...

The (n+1)×(n+1) tridiagonal matrix (also called the Clement matrix) defined by S_n=[0 n 0 0 ... 0; 1 0 n-1 0 ... 0; 0 2 0 n-2 ... 0; | | ... ... ... |; 0 0 0 n-1 0 1; 0 0 0 0 ...

The orchard-planting problem (also known as the orchard problem or tree-planting problem) asks that n trees be planted so that there will be r(n,k) straight rows with k trees ...

The number of cells in a generalized Chinese checkers board (or "centered" hexagram). Unlike the polygonal numbers, there is ambiguity in the case of the star numbers as to ...

A convex polyomino containing at least one edge of its minimal bounding rectangle. The perimeter and area generating function for directed polygons of width m, height n, and ...

An orthogonal coordinate system is a system of curvilinear coordinates in which each family of surfaces intersects the others at right angles. Orthogonal coordinates ...

The regular polygon of 17 sides is called the heptadecagon, or sometimes the heptakaidecagon. Gauss proved in 1796 (when he was 19 years old) that the heptadecagon is ...

The problem of determining how many nonattacking kings can be placed on an n×n chessboard. For n=8, the solution is 16, as illustrated above (Madachy 1979). In general, the ...