Bob Proctor Professor of Mathematics University of North Carolina

Go to the page for:
Let's Expand Rota's Twelvefold Way For Counting Partitions!

(This proposed American Mathematical Monthly article is the reference for my remarks in the On-Line Encyclopedia of Integer Sequences on partition counts. These appear in the OEIS after you scroll to the bottom of the 'Par' screen of the OEIS alphabetical index.)

Chapel Hill Poset Atlas (leaves this site and goes to a separate site)

d-Complete Posets Generalize Young Diagrams

The following two theorems extend the realms of the hook length and jeu de taquin properties from the non-trivial classes of posets historically known to possess these properties (shapes, shifted shapes, and rooted trees) to one much larger unifying class of posets.

Theorem 1:
Every d-complete poset has the jeu de taquin property.

Theorem 2: (Dale Peterson - B.P.)
Every d-complete poset has the hook length property.

Corollary to Theorem 2:
The number of order extensions of a d-complete poset is given by a hook length product formula which generalizes the famous Frame-Robinson-Thrall formula for the number of standard Young tableaux on a given shape.

Click here for as little or as much of an Exposition of These Results as you desire,

or click here for a list of selected publications.

Contact Information

Office: Phillips Hall 390

Email: rap =at= email.unc.edu

Research Interests

I primarily work in an area of overlap between combinatorics and representations of Lie algebras. From the combinatorial side, some of the objects which arise include Young tableaux, plane partitions, posets, generating functions, and enumeration formulas. From the representation side, some of the objects which arise include roots of Lie algebras, weights and characters of representations, and explicit actions of Lie algebras in representations, sometimes realized with posets.

Mailing Address

Math Dept, CB #3250 /// Univ of No Carolina /// Chapel Hill, NC 27599 /// USA

Link up to UNC Mathematics Department home page.