Name
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 n - 3 . 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. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1016/j.jcta.2013.09.010 | J. Comb. Theory, Ser. A |
Keywords | Field | DocType |
order complex,order congruence,combinatorial algebraic topology,nontrivial order congruence,linear extension,finite n-element poset p,dimension n-3,order-preserving poset partition,finite poset,cyclic class,homotopy equivalent,homology,poset | Discrete mathematics,Combinatorics,Interval order,Algebraic topology,Lattice (order),Graded poset,Linear extension,Homotopy,Congruence relation,Partially ordered set,Mathematics | Journal |
Volume | Issue | ISSN |
122 | C | 0097-3165 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gejza Jenča | 1 | 36 | 10.14 |
| Peter Sarkoci | 2 | 113 | 12.64 |