• Corpus ID: 220347398

Balanced squeezed Complexes

@article{JuhnkeKubitzke2020BalancedSC,
  title={Balanced squeezed Complexes},
  author={Martina Juhnke-Kubitzke and Uwe Nagel},
  journal={arXiv: Combinatorics},
  year={2020}
}
Given any order ideal $U$ consisting of color-squarefree monomials involving variables with $d$ colors, we associate to it a balanced $(d-1)$-dimensional simplicial complex $\Delta_{\mathrm{bal}}(U)$ that we call a balanced squeezed complex. In fact, these complexes have properties similar to squeezed balls as introduced by Kalai and the more general squeezed complexes, introduced by the authors. We show that any balanced squeezed complex is vertex-decomposable and that its flag $h$-vector can… 

References

SHOWING 1-10 OF 30 REFERENCES
A generalized lower bound theorem for balanced manifolds
A simplicial complex of dimension $$d-1$$d-1 is said to be balanced if its graph is d-colorable. Juhnke-Kubitzke and Murai proved an analogue of the generalized lower bound theorem for balanced
Squeezed complexes
Given a shifted order ideal U , we associate to it a family of simplicial complexes (Δt(U))t⩾0 that we call squeezed complexes. In a special case, our construction gives squeezed balls that were
Balanced complexes and complexes without large missing faces
The face numbers of simplicial complexes without missing faces of dimension larger than i are studied. It is shown that among all such (d−1)-dimensional complexes with non-vanishing top homology, a
Decompositions of Simplicial Complexes Related to Diameters of Convex Polyhedra
TLDR
It is shown that several cases in which the Hirsch conjecture has been verified can be handled by these methods, which also give the shellability of a number of simplicial complexes of combinatorial interest.
Betti numbers of strongly color-stable ideals and squarefree strongly color-stable ideals
Abstract In this paper, we will show that the color-squarefree operation does not change the graded Betti numbers of strongly color-stable ideals. In addition, we will give an example of a nonpure
Balanced generalized lower bound inequality for simplicial polytopes
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,
Many triangulated spheres
  • G. Kalai
  • Mathematics
    Discret. Comput. Geom.
  • 1988
TLDR
A construction of Billera and Lee is extended to obtain a large family of triangulated spheres and it is proved that logs(n) =20.69424n(1+o(1)).
...
1
2
3
...