## 38 Citations

Separation-type combinatorial invariants for triangulations of manifolds

- Mathematics
- 2018

We propose and study a variation of Bagchi and Datta's $\sigma$-vector of a simplicial complex C, whose entries are defined as weighted sums of Betti numbers of induced subcomplexes of C. We prove…

On Walkup’s class K(d) and a minimal triangulation of (S ⋉S)

- Mathematics
- 2013

For d ≥ 2, Walkup’s class K(d) consists of the d-dimensional simplicial complexes all whose vertex-links are stacked (d − 1)-spheres. Kalai showed that for d ≥ 4, all connected members of K(d) are…

A ug 2 01 2 Tight triangulations of some 4-manifolds

- Mathematics
- 2017

Walkup’s class K(d) consists of the d-dimensional simplicial complexes all whose vertex links are stacked (d − 1)-spheres. According to a result of Walkup, the face vector of any triangulated…

The mu vector, Morse inequalities and a generalized lower bound theorem for locally tame combinatorial manifolds

- MathematicsEur. J. Comb.
- 2016

M ay 2 01 3 On k-stellated and k-stacked spheres

- Mathematics
- 2013

We introduce the class Σk(d) of k-stellated (combinatorial) spheres of dimension d (0 ≤ k ≤ d+1) and compare and contrast it with the class Sk(d) (0 ≤ k ≤ d) of k-stacked homology d-spheres. We have…

Face numbers of manifolds with boundary

- Mathematics
- 2015

We study face numbers of simplicial complexes that triangulate manifolds (or even normal pseudomanifolds) with boundary. Specifically, we establish a sharp lower bound on the number of interior edges…

## References

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FACE ENUMERATION - FROM SPHERES TO MANIFOLDS

- Mathematics
- 2007

We prove a number of new restrictions on the enumerative properties of homology manifolds and semi-Eulerian complexes and posets. These include a determination of the affine span of the fine h-vector…

The lower bound conjecture for 3- and 4-manifolds

- Mathematics
- 1970

For any closed connected d-manifold M let ](M) denote the set of vectors / (K)= (]0(K) ..... fd(K)), where K ranges over all triangulations of M and ]k(K) denotes the number of k-simplices of K. The…

Minimal triangulations of sphere bundles over the circle

- MathematicsJ. Comb. Theory, Ser. A
- 2008

On stellated spheres, shellable balls, lower bounds and a combinatorial criterion for tightness

- Mathematics
- 2011

We introduce the $k$-stellated spheres and compare and contrast them with $k$-stacked spheres. It is shown that for $d \geq 2k$, any $k$-stellated sphere of dimension $d$ bounds a unique and…

Stacked polytopes and tight triangulations of manifolds

- MathematicsJ. Comb. Theory, Ser. A
- 2011

Rigidity and the lower bound theorem 1

- Mathematics
- 1987

SummaryFor an arbitrary triangulated (d-1)-manifold without boundaryC withf0 vertices andf1 edges, define
$$\gamma (C) = f_1 - df_0 + \left( {\begin{array}{*{20}c} {d + 1} \\ 2 \\ \end{array} }…

Enumerative properties of triangulations of spherical bundles over S1

- MathematicsEur. J. Comb.
- 2008

The 9-vertex complex projective plane

- Mathematics
- 1983

In the early days of topology, most of the objects of interest were defined in terms of triangulations, describing a topological space as a union of finitely many vertices, edges, triangles, and…