Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6424467 | Journal of Combinatorial Theory, Series A | 2014 | 11 Pages |
Abstract
We examine the lattice of all order congruences of a finite poset from the viewpoint of combinatorial algebraic topology. We prove that the order complex of the lattice of all nontrivial order congruences (or order-preserving partitions) of a finite n-element poset P with n⩾3 is homotopy equivalent to a wedge of spheres of dimension nâ3. If P is connected, then the number of spheres is equal to the number of linear extensions of P. In general, the number of spheres is equal to the number of cyclic classes of linear extensions of P.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Gejza JenÄa, Peter Sarkoci,