1. CMB 2013 (vol 57 pp. 225)
||Small Flag Complexes with Torsion|
We classify flag complexes on at most $12$ vertices with torsion in
the first homology group. The result is moderately computer-aided.
As a consequence we confirm a folklore conjecture that the smallest
poset whose order complex is homotopy equivalent to the real
projective plane (and also the smallest poset with torsion in the
first homology group) has exactly $13$ elements.
Keywords:clique complex, order complex, homology, torsion, minimal model
Categories:55U10, 06A11, 55P40, 55-04, 05-04
2. CMB 2007 (vol 50 pp. 182)
||On the Coxeter Transformations for Tamari Posets |
A relation between the anticyclic structure of the dendriform operad
and the Coxeter transformations in the Grothendieck groups of the
derived categories of modules over the Tamari posets is obtained.
Categories:18D50, 18E30, 06A11