Abstract
We apply the homomorphism complex construction to partially ordered sets, introducing a new topological construction based on the set of maximal chains in a graded poset. Our primary objects of study are distributive lattices, with special emphasis on finite products of chains. For the special case of a Boolean algebra, we observe that the corresponding homomorphism complex is isomorphic to the subcomplex of cubical cells in a permutahedron. Thus, this work can be interpreted as a generalization of the study of these complexes. We provide a detailed investigation when our poset is a product of chains, in which case we find an optimal discrete Morse matching and prove that the corresponding complex is torsion-free.
Original language | English |
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Pages (from-to) | 178-194 |
Number of pages | 17 |
Journal | European Journal of Combinatorics |
Volume | 81 |
DOIs | |
State | Published - Oct 2019 |
Bibliographical note
Publisher Copyright:© 2019 Elsevier Ltd
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics