John Shareshian
A new subgroup lattice characterization of finite solvable groups.
Fri, 11/12/2010 - 16:01 — SomNambulAuthors: John Shareshian, Russ Woodroofe
Subjects: Group Theory
AbstractWe show that if G is a finite group then no chain of modular elements in its
subgroup lattice L(G) is longer than a chief series. Also, we show that if G is
a nonsolvable finite group then every maximal chain in L(G) has length at least
two more than that of the chief length of G, thereby providing a converse of a
result of J. Kohler.Eulerian quasisymmetric functions and cyclic sieving.
Fri, 09/18/2009 - 11:36 — SomNambulAuthors: Bruce Sagan, John Shareshian, Michelle L. Wachs
Subjects: Combinatorics
AbstractIt is shown that a refined version of a q-analogue of the Eulerian numbers
together with the action, by conjugation, of the subgroup of the symmetric
group $S_n$ generated by the $n$-cycle $(1,2,...,n)$ on the set of permutations
of fixed cycle type and fixed number of excedances provides an instance of the
cyclic sieving phenonmenon of Reiner, Stanton and White. The main tool is a
class of symmetric functions recently introduced in work of two of the authors.
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