Face enumeration on simplicial complexes. (English) Zbl 1354.05152
Beveridge, Andrew (ed.) et al., Recent trends in combinatorics. Cham: Springer (ISBN 978-3-319-24296-5/hbk; 978-3-319-24298-9/ebook). The IMA Volumes in Mathematics and its Applications 159, 653-686 (2016).
Summary: In this chapter we survey many exciting developments on the face numbers of simplicial complexes from the past two decades. We focus on simplicial complexes whose geometric realizations are (homology) manifolds, as well as manifolds with additional combinatorial structure such as balanced manifolds or flag manifolds. The discussed results range from the Upper Bound Theorem for manifolds to the balanced Generalized Lower Bound Theorem for balanced polytopes.
For the entire collection see [Zbl 1348.05002].
For the entire collection see [Zbl 1348.05002].
MSC:
| 05E45 | Combinatorial aspects of simplicial complexes |
| 13F55 | Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes |
| 57Q15 | Triangulating manifolds |
