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For any constructible function f, there exists a function P_f such that for all functions t, the following two statements are equivalent: 1. There exists an algorithm A such ...

Let k>=0 and n>=2 be integers. A SOMA, or more specifically a SOMA(k,n), is an n×n array A, whose entries are k-subsets of a kn-set Omega, such that each element of Omega ...

A curve named and studied by Newton in 1701 and contained in his classification of cubic curves. It had been studied earlier by L'Hospital and Huygens in 1692 (MacTutor ...

Let a simple graph G have n vertices, chromatic polynomial P(x), and chromatic number chi. Then P(G) can be written as P(G)=sum_(i=0)^ha_i·(x)_(p-i), where h=n-chi and (x)_k ...

The Suetake graph is a weakly regular Hamiltonian graph on 231 vertices with parameters (nu,k,lambda,mu)=(72,(12),(0),(0,4)). It is distance-regular with intersection array ...

A finite simple group of Lie-type. The following table summarizes the types of twisted Chevalley groups and their respective orders. In the table, q denotes a prime power and ...

Logic is the formal mathematical study of the methods, structure, and validity of mathematical deduction and proof. According to Wolfram (2002, p. 860), logic is the most ...

A set is a finite or infinite collection of objects in which order has no significance, and multiplicity is generally also ignored (unlike a list or multiset). Members of a ...

An algebraic surface of order 3. Schläfli and Cayley classified the singular cubic surfaces. On the general cubic, there exists a curious geometrical structure called double ...

A symmetric graph is a graph that is both edge- and vertex-transitive (Holton and Sheehan 1993, p. 209). However, care must be taken with this definition since arc-transitive ...