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The Motzkin numbers enumerate various combinatorial objects. Donaghey and Shapiro (1977) give 14 different manifestations of these numbers. In particular, they give the ...

The Neuberg cubic Z(X_(30)) of a triangle DeltaABC is the locus of all points P whose reflections in the sidelines BC, CA, and ABform a triangle perspective to DeltaABC. It ...

If all the diagonals--including those obtained by "wrapping around" the edges--of a magic square sum to the same magic constant, the square is said to be a panmagic square ...

Given any straight line and a point not on it, there "exists one and only one straight line which passes" through that point and never intersects the first line, no matter ...

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides is called a rhombus, and a ...

A planar straight line embedding of a planar graph is a planar embedding in which only straight line segments are used to connect the graph vertices. Fáry (1948) showed that ...

Poker is a card game played with a normal deck of 52 cards. Sometimes, additional cards called "jokers" are also used. In straight or draw poker, each player is normally ...

A polyomino tiling is a tiling of the plane by specified types of polyominoes. Tiling by polyominoes has been investigated since at least the late 1950s, particularly by S. ...

A prime partition of a positive integer n>=2 is a set of primes p_i which sum to n. For example, there are three prime partitions of 7 since 7=7=2+5=2+2+3. The number of ...

A primitive polynomial is a polynomial that generates all elements of an extension field from a base field. Primitive polynomials are also irreducible polynomials. For any ...