Rodica Simion's Short Description of Her Research

Rodica Simion

   In the last few decades numerous connections between combinatorics and
   other subjects - such as algebra, topology, geometry, and theoretical
   computer science - have led to remarkable developments. Among these is
   the evolution of enumeration, perhaps the most fundamental aspect of
   combinatorics and that with the longest tradition. Enumeration is the
   subject of counting the elements of a finite set of discrete
   structures and investigating properties of the resulting numbers.
   Particularly since the 1960's, the enumeration of combinatorial
   objects has come to involve questions and tools from subjects such as
   the theory of partially ordered sets, symmetric functions and
   representation theory, algebraic topology, and algebraic geometry.
   
   Some of the many tantalizing directions of current research in
   enumeration are related to partially ordered sets, Coxeter systems,
   and convex polytopes. In these contexts, one of the goals is to obtain
   refined enumeration results, according to natural combinatorial
   statistics (``q-enumeration''). Another is to provide a unified and
   systematic treatment encompassing enumeration results for classical
   combinatorial objects and their generalizations to settings of
   algebraic or geometric interest (e.g., the symmetric group or
   partitions vs. Weyl groups or arrangements of subspaces). Still
   another theme is to deepen the understanding of enumeratively defined
   invariants (e.g., the flag f-vector and cd-index of a polytope or of
   an Eulerian partially ordered set).
   
  Selected Publications
  
     * Combinatorial statistics on non-crossing partitions, J. Combin.
       Theory Series A 66 (1994) 270-301.
     * On q-analogues of partially ordered sets, J. Combin. Theory Series
       A, to appear.
     * Octabasic Laguerre polynomials and permutation statistics,
       co-authored with D. Stanton, J. Computational and Applied
       Mathematics, to appear.
     * Le numbers of arrangements and matroid identities, co-authored
       with D. Massey, R. Stanley, D. Vertigan, D. Welsh, and G. Ziegler,
       submitted manuscript.