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A monoid is a set that is closed under an associative binary operation and has an identity element I in S such that for all a in S, Ia=aI=a. Note that unlike a group, its ...

Given three curves phi_1, phi_2, phi_3 with the common group of ordinary points G (which may be empty), let their remaining groups of intersections g_(23), g_(31), and g_(12) ...

The Balaban index J is a graph index defined for a graph on n nodes, m edges, and c connected components by J=m/(gamma+1)sum_((i,j) in E(G))(D_iD_j)^(-1/2), where gamma=m-n+c ...

A lucky number of Euler is a number p such that the prime-generating polynomial n^2-n+p is prime for n=1, 2, ..., p-1. Such numbers are related to the imaginary quadratic ...

Serre's problem, also called Serre's conjecture, asserts that the implication "free module ==> projective module" can be reversed for every module over the polynomial ring ...

A technical mathematical object defined in terms of a polynomial ring of n variables over a field k. Syzygies occur in tensors at rank 5, 7, 8, and all higher ranks, and play ...

In general, a topological index, sometimes also known as a graph-theoretic index, is a numerical invariant of a chemical graph (Plavšić et al. 1993). Particular topological ...

A monoid that is commutative i.e., a monoid M such that for every two elements a and b in M, ab=ba. This means that commutative monoids are commutative, associative, and have ...

The product of a family {X_i}_(i in I) of objects of a category is an object P=product_(i in I)X_i, together with a family of morphisms {p_i:P->X_i}_(i in I) such that for ...

The Livingstone graph is a distance-transitive graph on 266 vertices defined in terms of the Janko group J_1. It has intersection array {11,10,6,1;1,1,5,11}. The Livingstone ...