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The projective general orthogonal group PGO_n(q) is the group obtained from the general orthogonal group GO_n(q) on factoring the scalar matrices contained in that group.

The projective special orthogonal group PSO_n(q) is the group obtained from the special orthogonal group SO_n(q) on factoring by the scalar matrices contained in that group. ...

Given a 111×111 (0,1)-matrix, fill 11 spaces in each row in such a way that all columns also have 11 spaces filled. Furthermore, each pair of rows must have exactly one ...

Given any assignment of n-element sets to the n^2 locations of a square n×n array, is it always possible to find a partial Latin square? The fact that such a partial Latin ...

A groupoid S such that for all a,b in S, there exist unique x,y in S such that ax = b (1) ya = b. (2) No other restrictions are applied; thus a quasigroup need not have an ...

A magic square-type arrangement of the words in the Latin sentence "Sator Arepo tenet opera rotas" ("the farmer Arepo keeps the world rolling"). This square has been found in ...

A glome is a 4-sphere (in the geometer's sense of the word) x^2+y^2+z^2+w^2=r^2 (as opposed to the usual 3-sphere). The term derives from the Latin "glomus" meaning "ball of ...

The quincunx is the pattern of five dots that appears on the "5" side of a 6-sided die. The word derives from the Latin words for both one and five. The Galton board is ...

A set of n cells in an n×n square such that no two come from the same row and no two come from the same column. The number of transversals of an n×n square is n! (n ...

Combinatorial matrix theory is a rich branch of mathematics that combines combinatorics, graph theory, and linear algebra. It includes the theory of matrices with prescribed ...