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Every nonconstant entire function attains every complex value with at most one exception (Henrici 1988, p. 216; Apostol 1997). Furthermore, every analytic function assumes ...

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 ...

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 ...

A generalization of the Kronecker decomposition theorem which states that every finitely generated Abelian group is isomorphic to the group direct sum of a finite number of ...

Let E be the largest and e the smallest power of l in the HOMFLY polynomial of an oriented link, and i be the braid index. Then the Morton-Franks-Williams inequality holds, ...

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} ...

The statistics h_(r,s,...) defined such that <h_(r,s,...)>=mu_rmu_s..., where mu_r is a central moment. These statistics generalize h-statistics and were originally called ...