Shellability of face posets of electrical networks and the CW poset property
| Autor: | Patricia Hersh, Richard Kenyon |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
05E45
06A07 05C83 Conjecture Mathematics::Combinatorics Applied Mathematics 010102 general mathematics Eulerian path Type (model theory) 01 natural sciences Bruhat order 010101 applied mathematics Combinatorics symbols.namesake Product (mathematics) symbols FOS: Mathematics Interval (graph theory) Mathematics - Combinatorics Product topology Combinatorics (math.CO) 0101 mathematics Partially ordered set Mathematics |
| Popis: | We prove a conjecture of Thomas Lam that the face posets of stratified spaces of planar resistor networks are shellable. These posets are called uncrossing partial orders. This shellability result combines with Lam's previous result that these same posets are Eulerian to imply that they are CW posets, namely that they are face posets of regular CW complexes. Certain subsets of uncrossing partial orders are shown to be isomorphic to type A Bruhat order intervals; our shelling is shown to coincide on these intervals with a Bruhat order shelling which was constructed by Matthew Dyer using a reflection order. Our shelling for uncrossing posets also yields an explicit shelling for each interval in the face posets of the edge product spaces of phylogenetic trees, namely in the Tuffley posets, by virtue of each interval in a Tuffley poset being isomorphic to an interval in an uncrossing poset. This yields a more explicit proof of the result of Gill, Linusson, Moulton and Steel that the CW decomposition of Moulton and Steel for the edge product space of phylogenetic trees is a regular CW decomposition. 26 pages, 5 figures; additional corollary to the main result added, namely an explicit shelling for each poset interval in the face poset for the edge product space of phylogenetic trees |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|