SB-labelings and posets with each interval homotopy equivalent to a sphere or a ball

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:152

Article

Hersh, Patricia¹  Meszaros, Karola² 

[1] North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

[2] Cornell Univ, Dept Math, White Hall, Ithaca, NY 14853 USA

关键词: Poset topology;    Mobius function;    Crosscut complex;    Tamari lattice;    Weak order;   

DOI  :  10.1016/j.jcta.2017.06.001

来源: Elsevier

【 摘 要 】

We introduce a new class of edge labelings for locally finite lattices which we call SB-labelings. We prove for finite lattices which admit an SB-labeling that each open interval has the homotopy type of a ball or of a sphere of some dimension. Natural examples include the weak order, the Tamari lattice, and the finite distributive lattices. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free