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
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.
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
Office: Phillips Hall 390
Email: rap =at= email.unc.edu
Office Phone: 919-962-9623
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.
Math Dept, CB #3250 /// Univ of No Carolina /// Chapel Hill, NC
27599 /// USA