Lincidence

Lincidence is a term with no single, widely accepted meaning in mainstream mathematics or science. In scholarly contexts it is sometimes used to discuss generalized incidence concepts or to illustrate what an incidence relation could look like if the standard objects were expanded beyond lines to a broader class of geometric or combinatorial objects. Because the term is not standard, its precise meaning varies by author and context.

A common way to describe lincidence hypothetically is to consider a structure consisting of a set P of points, a set O of objects (which could be lines, curves, planes, or higher-dimensional analogues), and an incidence relation I subset of P × O that records which points lie on which objects. Such a framework would generalize classical incidence geometry, potentially altering axioms about how many points may lie on a given object or how many objects pass through a point. In this sense, lincidence could be viewed as a conceptual generalization rather than a defined theory with fixed postulates.

In practice, the term is mostly seen in discussions about generalizations, pedagogical contrasts, or in fictional or speculative literature. It is not part of standard mathematical terminology, and there are no formal, universally accepted definitions or theorems attached to it. Outside mathematics, Lincidence can be a proper noun, used as a brand, project name, or surname, unrelated to geometry. See also incidence geometry, incidence structure, and block design.