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