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An ordering for the Cartesian product × of any two sets A and B with order relations <A and <B, respectively, such that if (a_1,b_1) and (a_2,b_2) both belong to A×B, then ...

In 1979, Conway and Norton discovered an unexpected intimate connection between the monster group M and the j-function. The Fourier expansion of j(tau) is given by (1) (OEIS ...

Given a commutative unit ring R and a filtration F:... subset= I_2 subset= I_1 subset= I_0=R (1) of ideals of R, the Rees ring of R with respect to F is R_+(F)=I_0 direct sum ...

Given rods of length 1, 2, ..., n, how many distinct triangles T(n) can be made? Lengths for which l_i>=l_j+l_k (1) obviously do not give triangles, but all other ...

A truth table is a two-dimensional array with n+1 columns. The first n columns correspond to the possible values of n inputs, and the last column to the operation being ...

A game played with two heaps of counters in which a player may take any number from either heap or the same number from both. The player taking the last counter wins. The rth ...

An operator defined on a set S which takes two elements from S as inputs and returns a single element of S. Binary operators are called compositions by Rosenfeld (1968). Sets ...

The symbol intersection , used for the intersection of sets, and sometimes also for the logical connective AND instead of the symbol ^ (wedge). In fact, for any two sets A ...

Let A^~, B^~, ... be operators. Then the commutator of A^~ and B^~ is defined as [A^~,B^~]=A^~B^~-B^~A^~. (1) Let a, b, ... be constants, then identities include [f(x),x] = 0 ...

Conjugation is the process of taking a complex conjugate of a complex number, complex matrix, etc., or of performing a conjugation move on a knot. Conjugation also has a ...