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A formula for the number of Young tableaux associated with a given Ferrers diagram. In each box, write the sum of one plus the number of boxes horizontally to the right and ...

The Krohn-Rhodes complexity, also called the group complexity or simply "the complexity," of a finite semigroup S is the smallest number of groups in a wreath product of ...

Pairs of points of a line, the product of whose distances from a fixed point is a given constant. This is more concisely defined as a projectivity of period two. If ...

A polynomial is called logarithmically concave (or log-concave) if the sequence of its coefficients is logarithmically concave. If P(x) is log-convex and Q(x) is unimodal, ...

The power A^n of a matrix A for n a nonnegative integer is defined as the matrix product of n copies of A, A^n=A...A_()_(n). A matrix to the zeroth power is defined to be the ...

Let pi_n(x)=product_(k=0)^n(x-x_k), (1) then f(x)=f_0+sum_(k=1)^npi_(k-1)(x)[x_0,x_1,...,x_k]+R_n, (2) where [x_1,...] is a divided difference, and the remainder is ...

A group G is nilpotent if the upper central sequence 1=Z_0<=Z_1<=Z_2<=...<=Z_n<=... of the group terminates with Z_n=G for some n. Nilpotent groups have the property that ...

An irreducible algebraic integer which has the property that, if it divides the product of two algebraic integers, then it divides at least one of the factors. 1 and -1 are ...

The derivative identity d/(dx)[f(x)g(x)] = lim_(h->0)(f(x+h)g(x+h)-f(x)g(x))/h (1) = (2) = lim_(h->0)[f(x+h)(g(x+h)-g(x))/h+g(x)(f(x+h)-f(x))/h] (3) = f(x)g^'(x)+g(x)f^'(x), ...

A relation is any subset of a Cartesian product. For instance, a subset of A×B, called a "binary relation from A to B," is a collection of ordered pairs (a,b) with first ...