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The mathematical study of abstract computing machines (especially Turing machines) and the analysis of algorithms used by such machines. A connection between automata theory ...

A k-automatic set is a set of integers whose base-k representations form a regular language, i.e., a language accepted by a finite automaton or state machine. If bases a and ...

A real vector bundle pi:E->M has an orientation if there exists a covering by trivializations U_i×R^k such that the transition functions are vector space ...

The Cauchy remainder is a different form of the remainder term than the Lagrange remainder. The Cauchy remainder after n terms of the Taylor series for a function f(x) ...

A plane partition whose solid Ferrers diagram is invariant under the rotation which cyclically permutes the x-, y-, and z-axes. Macdonald's plane partition conjecture gives a ...

A method of determining coefficients alpha_k in a power series solution y(x)=y_0(x)+sum_(k=1)^nalpha_ky_k(x) of the ordinary differential equation L^~[y(x)]=0 so that ...

The number of elements in a group G, denoted |G|. If the order of a group is a finite number, the group is said to be a finite group. The order of an element g of a finite ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), define the Hilbert function of M as the map ...

Consider a power series in a complex variable z g(z)=sum_(n=0)^inftya_nz^n (1) that is convergent within the open disk D:|z|<R. Convergence is limited to within D by the ...

Let 0<p_1<p_2<... be integers and suppose that there exists a lambda>1 such that p_(j+1)/p_j>lambda for j=1, 2, .... Suppose that for some sequence of complex numbers {a_j} ...