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A matrix for a round-robin tournament involving n players competing in n(n-1)/2 matches (no ties allowed) having entries a_(ij)={1 if player i defeats player j; -1 if player ...

A tripod is a tree having exactly three tree leaves (Pirnazar and Ullman 2002). The numbers of tripods on n=1, 2, ... vertices are 0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, ...

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 ...

The Game of Logic, described by Lewis Carroll--author of Alice in Wonderland--in 1887 (Carroll 1972) consists of discussing the meaning of propositions like "Some fresh cakes ...

There are no fewer than two closely related but somewhat different notions of gerbe in mathematics. For a fixed topological space X, a gerbe on X can refer to a stack of ...

A set-theoretic term having a number of different meanings. Fraenkel (1953, p. 37) used the term as a synonym for "finite set." However, according to Russell's definition ...

A mathematical statement that one quantity is greater than or less than another. "a is less than b" is denoted a<b, and "a is greater than b" is denoted a>b. "a is less than ...

An interpretation of first-order logic consists of a non-empty domain D and mappings for function and predicate symbols. Every n-place function symbol is mapped to a function ...

Let (a)_i and (b)_i be sequences of complex numbers such that b_j!=b_k for j!=k, and let the lower triangular matrices F=(f)_(nk) and G=(g)_(nk) be defined as ...

A (general, asymmetric) lens is a lamina formed by the intersection of two offset disks of unequal radii such that the intersection is not empty, one disk does not completely ...