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A p-system of a set S is a sequence of subsets A_1, A_2, ..., A_p of S, among which some may be empty or coinciding with each other.

An arithmetic series is the sum of a sequence {a_k}, k=1, 2, ..., in which each term is computed from the previous one by adding (or subtracting) a constant d. Therefore, for ...

Find the maximum number of bishops B(n) that can be placed on an n×n chessboard such that no two attack each other. The answer is 2n-2 (Dudeney 1970, Madachy 1979), giving ...

The Blancmange function, also called the Takagi fractal curve (Peitgen and Saupe 1988), is a pathological continuous function which is nowhere differentiable. Its name ...

A chain complex is a sequence of maps ...-->^(partial_(i+1))C_i-->^(partial_i)C_(i-1)-->^(partial_(i-1))..., (1) where the spaces C_i may be Abelian groups or modules. The ...

An algebraic surface with affine equation P_d(x_1,x_2)+T_d(x_3)=0, (1) where T_d(x) is a Chebyshev polynomial of the first kind and P_d(x_1,x_2) is a polynomial defined by ...

A problem sometimes known as Moser's circle problem asks to determine the number of pieces into which a circle is divided if n points on its circumference are joined by ...

The complementary subspace problem asks, in general, which closed subspaces of a Banach space are complemented (Johnson and Lindenstrauss 2001). Phillips (1940) proved that ...

The homomorphism S which, according to the snake lemma, permits construction of an exact sequence (1) from the above commutative diagram with exact rows. The homomorphism S ...

Conway's soldiers, also known as the "solitaire army" game (Berlekamp et al. 1982) or "checker-jumping problem" (Honsberger 1976) is a one-player game played on an infinite ...