TY - JOUR
T1 - Balanced generalized lower bound inequality for simplicial polytopes
AU - Juhnke-Kubitzke, Martina
AU - Murai, Satoshi
N1 - Funding Information:
Acknowledgements The first author was partially supported by DFG GK-1916. The second author was partially supported by JSPS KAKENHI 25400043. We would like to thank Steven Klee and Isabella Novik for their helpful comments on the paper.
Publisher Copyright:
© 2017, Springer International Publishing AG.
PY - 2018/4/1
Y1 - 2018/4/1
N2 - A remarkable and important property of face numbers of simplicial polytopes is the generalized lower bound inequality, which says that the h-numbers of any simplicial polytope are unimodal. Recently, for balanced simplicial d-polytopes, that is simplicial d-polytopes whose underlying graphs are d-colorable, Klee and Novik proposed a balanced analogue of this inequality, that is stronger than just unimodality. The aim of this article is to prove this conjecture of Klee and Novik. For this, we also show a Lefschetz property for rank-selected subcomplexes of balanced simplicial polytopes and thereby obtain new inequalities for their h-numbers.
AB - A remarkable and important property of face numbers of simplicial polytopes is the generalized lower bound inequality, which says that the h-numbers of any simplicial polytope are unimodal. Recently, for balanced simplicial d-polytopes, that is simplicial d-polytopes whose underlying graphs are d-colorable, Klee and Novik proposed a balanced analogue of this inequality, that is stronger than just unimodality. The aim of this article is to prove this conjecture of Klee and Novik. For this, we also show a Lefschetz property for rank-selected subcomplexes of balanced simplicial polytopes and thereby obtain new inequalities for their h-numbers.
KW - 05C15
KW - 13F55
KW - 52B05
UR - http://www.scopus.com/inward/record.url?scp=85031785172&partnerID=8YFLogxK
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U2 - 10.1007/s00029-017-0363-1
DO - 10.1007/s00029-017-0363-1
M3 - Article
AN - SCOPUS:85031785172
SN - 1022-1824
VL - 24
SP - 1677
EP - 1689
JO - Selecta Mathematica, New Series
JF - Selecta Mathematica, New Series
IS - 2
ER -