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If n=1,2 (mod 4), and the squarefree part of n is divisible by a prime p=3 (mod 4), then no difference set of order n exists. Equivalently, if a projective plane of order n ...
For any alpha in A (where A denotes the set of algebraic numbers), let |alpha|^_ denote the maximum of moduli of all conjugates of alpha. Then a function ...
Let L denote the partition lattice of the set {1,2,...,n}. The maximum element of L is M={{1,2,...,n}} (1) and the minimum element is m={{1},{2},...,{n}}. (2) Let Z_n denote ...
A Pythagorean quadruple is a set of positive integers a, b, c, and d that satisfy a^2+b^2+c^2=d^2. (1) For positive even a and b, there exist such integers c and d; for ...
Let G be an undirected graph, and let i denote the cardinal number of the set of externally active edges of a spanning tree T of G, j denote the cardinal number of the set of ...
A number n is called a barrier of a number-theoretic function f(m) if, for all m<n, m+f(m)<=n. Neither the totient function phi(n) nor the divisor function sigma(n) has a ...
An equalizer of a pair of maps f,g:X->Y in a category is a map e:E->X such that 1. f degreese=g degreese, where degrees denotes composition. 2. For any other map e^':E^'->X ...
The kth power of a graph G is a graph with the same set of vertices as G and an edge between two vertices iff there is a path of length at most k between them (Skiena 1990, ...
The spectrum of a ring is the set of proper prime ideals, Spec(R)={p:p is a prime ideal in R}. (1) The classical example is the spectrum of polynomial rings. For instance, ...
The first and second Zagreb indices for a graph with vertex count n and vertex degrees v_i for i=1, ..., n are defined by Z_1=sum_(i=1)^nv_i^2 and Z_2=sum_((i,j) in ...
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