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Cointerval Complexes and Complexes of Ordered Homomorphisms
Algebra & Discrete Mathematics| Speaker: | Steve Klee, UC Davis |
| Location: | 1147 MSB |
| Start time: | Fri, Oct 22 2010, 2:10PM |
Description
We introduce the class of cointerval simplicial complexes, which
generalize the classes of cointerval hypergraphs, introducedby
Dochterman and Engstr\"{o}m, and shifted simplicial complexes,
introduced by Erd\H{o}s-Ko-Rado (combinatorial shifting) and Kalai
(algebraic shifting). We will discuss some geometric properties of
cointerval complexes, and introduce a (polyhedral) complex of
order-preserving homomorphisms, $OHOM (\Gamma, \Delta)$, between
simplicial complexes $\Gamma$ and $\Delta$. We will show that the
complex $OHOM (\Gamma,\Delta)$ supports a minimal free resolution of
an associated monomial ideal when $\Delta$ is a cointerval simplicial
complex. This work is joint with Jonathan Browder and Benjamin Braun.