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An alternating sign matrix is a matrix of 0s, 1s, and -1s in which the entries in each row or column sum to 1 and the nonzero entries in each row and column alternate in ...

An out-shuffle, also known as a perfect shuffle (Golomb 1961), is a riffle shuffle in which the top half of the deck is placed in the right hand, and cards are then ...

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" octahedral graph is the 6-node 12-edge Platonic graph having the connectivity of the octahedron. It is isomorphic to the circulant graph Ci_6(1,2), the cocktail party ...

The likelihood of a simple graph is defined by starting with the set S_1={(K_11)}. The following procedure is then iterated to produce a set of graphs G_n of order n. At step ...

An analog of the polyominoes and polyiamonds in which collections of regular hexagons are arranged with adjacent sides. They are also called hexes, hexas, or polyfrobs ...

The Sierpiński gasket graph of order n is the graph obtained from the connectivity of the Sierpiński sieve. The first few Sierpiński gasket graphs are illustrated above. S_2 ...

A unit-distance graph is a distance graph having an embedding in the Euclidean plane (unit-distance embedding) in which vertices are distinct points and all edges are of ...

A Hamiltonian cycle, also called a Hamiltonian circuit, Hamilton cycle, or Hamilton circuit, is a graph cycle (i.e., closed loop) through a graph that visits each node ...

The cycloid is the locus of a point on the rim of a circle of radius a rolling along a straight line. It was studied and named by Galileo in 1599. Galileo attempted to find ...