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Consider the plane quartic curve X defined by x^3y+y^3z+z^3x=0, where homogeneous coordinates have been used here so that z can be considered a parameter (the plot above ...

A primitive root of a prime p is an integer g such that g (mod p) has multiplicative order p-1 (Ribenboim 1996, p. 22). More generally, if GCD(g,n)=1 (g and n are relatively ...

A circle having a given number of lattice points on its circumference. The Schinzel circle having n lattice points is given by the equation {(x-1/2)^2+y^2=1/45^(k-1) for n=2k ...

Two numbers are heterogeneous if their prime factors are distinct. For example, 6=2·3 and 24=2^3·3 are not heterogeneous since their factors are each (2, 3).

The cubeplex graph is the cubic Hamiltonian graph on 12 nodes illustrated above in several embeddings and corresponding to the graph Gamma_1 in Fischer and Little (2001). It ...

The cubitruncated cuboctahedron (called the cubotruncated cuboctahedron by Wenninger 1971, p. 121) is the uniform polyhedron with Maeder index 16 (Maeder 1997), Wenninger ...

700 The great dodecahemicosahedron is the uniform polyhedron with Maeder index 65 (Maeder 1997), Wenninger index 102 (Wenninger 1989), Coxeter index 81 (Coxeter et al. 1954), ...

The Van Lint-Schrijver Graph graph is a weakly regular Hamiltonian graph on 162 vertices with parameters (nu,k,lambda,mu)=(162,(6),(0),(0,1)). It is distance-regular with ...

A 1-variable unoriented knot polynomial Q(x). It satisfies Q_(unknot)=1 (1) and the skein relationship Q_(L_+)+Q_(L_-)=x(Q_(L_0)+Q_(L_infty)). (2) It also satisfies ...

A Cayley tree is a tree in which each non-leaf graph vertex has a constant number of branches n is called an n-Cayley tree. 2-Cayley trees are path graphs. The unique ...