Chapel Hill Poset Atlas

Cheryl A. Gann and Robert A. Proctor

August 3, 2005

Data Contents

This site contains lists of the following kinds of posets with up to m elements:
m=9: Unlabeled posets, connected posets, and posets with unique maximal elements.
m=9: Connected hook length posets and indecomposable disconnected hook length posets.
m=9: Connected d-complete and connected jeu de taquin posets.
m=7: Naturally labeled posets and hook length posets.

The following data is listed for posets with up to 7 elements:
Inverse order extensions, isomorphisms from natural labellings to standard forms, and name lookups for standard forms.


* Concise easily human-readable data structure for each poset.
* Each poset is expressed in a unique standard form.
* Posets are easily readably listed in a standard order, one poset per line.
* Direct web access to individual data files: preview and download only those you want.
* Data in Mathematica form, and should be easily convertible to other forms.
* Auxiliary data for fast isomorphism and order extension computations.
* Carefully checked data.
* The Mathematica programs used to generate this data may be downloaded.

Table of Contents

Poset Definitions
Poset Counts
Data Structure for Posets
Standard Forms for Posets & Standard Ordering of Standard Forms
Definitions for Associated Data Files

Access to Poset List Files and Associated Data Files

Cheryl Gann's 2005 UNC-CH Masters Project
Access to Program Files

This site is maintained (Maintenance Log) by Bob Proctor: rap =at=
His home page at a separate website contains a hypertext overview of d-complete posets and of jeu de taquin posets. Find it by searching for "Mathematician Robert A. Proctor's Home Page".

This site builds upon work done by David M. Behrman and Sarah Wilmesmeier Bergmann in their 1996-97 UNC Masters projects.

Please cite this site! (If it was helpful for your research.)
[*] C.A. Gann and R.A. Proctor, Chapel Hill Poset Atlas,
published electronically at, v 1.0, July 2005.

John Stembridge has posted a poset computational system which consists of many Maple programs. It also contains some lists of posets and lattices, some of which we have used to check our work. Find it by searching for "Stembridge's Maple packages for posets".

Curtis Greene, et. al., have posted a poset computational package which consists of many Mathematica programs. Find it by searching for "Greene's Mathematica Package for Posets".