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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 ...

Given a triangle, extend two sides in the direction opposite their common vertex. The circle tangent to these two lines and to the other side of the triangle is called an ...

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 ...

Every finite Abelian group can be written as a group direct product of cyclic groups of prime power group orders. In fact, the number of nonisomorphic Abelian finite groups ...

The Laguerre polynomials are solutions L_n(x) to the Laguerre differential equation with nu=0. They are illustrated above for x in [0,1] and n=1, 2, ..., 5, and implemented ...

The quotient W(p)=((p-1)!+1)/p which must be congruent to 0 (mod p) for p to be a Wilson prime. The quotient is an integer only when p=1 (in which case W(1)=2) or p is a ...

The incenter I is the center of the incircle for a polygon or insphere for a polyhedron (when they exist). The corresponding radius of the incircle or insphere is known as ...

Schmidt (1993) proposed the problem of determining if for any integer r>=2, the sequence of numbers {c_k^((r))}_(k=1)^infty defined by the binomial sums sum_(k=0)^n(n; ...

Let A be an n×n real square matrix with n>=2 such that |sum_(i=1)^nsum_(j=1)^na_(ij)s_it_j|<=1 (1) for all real numbers s_1, s_2, ..., s_n and t_1, t_2, ..., t_n such that ...

Given a simplex of unit content in Euclidean d-space, pick n>=d+1 points uniformly and independently at random, and denote the expected content of their convex hull by ...