Locally finite poset

In mathematics, a locally finite poset is a partially ordered set P such that for all x, y  P, the interval [x, y] consists of finitely many elements.

Given a locally finite poset P we can define its incidence algebra. Elements of the incidence algebra are functions ƒ that assign to each interval [x, y] of P a real number ƒ(x, y). These functions form an associative algebra with a product defined by

There is also a definition of incidence coalgebra.

In theoretical physics a locally finite poset is also called a causal set and has been used as a model for spacetime.

References

Stanley, Richard P. Enumerative Combinatorics, Volume I. Cambridge University Press, 1997. Pages 98, 113–116.


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.