Polyhedral geometry and partition theory
November 7 to November 11, 2016
American Institute of Mathematics,
San Jose, California
and Carla D. Savage
This workshop will be devoted to the study of
problems at the interface of polyhedral geometry and partition theory. Recent
results have demonstrated that polyhedral geometry is a powerful tool connecting
problems in lattice point enumeration, permutation statistics, and partition
theory. Further intriguing relationships make it clear that there are deeper
connections, both theoretical and computational, to be uncovered.
The main topics for our workshop include:
- the geometric and algebraic structure of lecture hall partitions; their
relationship to permutation and Coxeter groups, (rational) Catalan
combinatorics, and hyperplane arrangements.
- the geometry, combinatorics, and computation of vector partition functions;
the interpretation and application of recent structural results; the discovery
of new formulas.
- unimodality/real rootedness questions in Ehrhart theory, partition theory,
and Coxeter groups.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.
Papers arising from the workshop: