A formula for the Euler characteristics of even dimensional triangulated manifolds

Abstract

Abstract. An alternative formula for the Euler characteristics of even dimensional triangulated manifolds is deduced from the generalized Dehn-Sommerville equations.

Asymptotic Measures and Links in Simplicial Complexes

“…We also observe the following theorem (see Corollary 9 and Theorem 12), the first part of which is a corollary of Theorem 1 which has been independently (not as a corollary of Theorem 1) observed by T. Akita [1].…”

“…Remark 10 The first part of Corollary 9 was independently (not as a corollary of Theorem 8) observed by T. Akita [1]. In [8], we provide a probabilistic proof of it.…”

“…where I h is the set defined in (1). We then set p 2 : (σ, τ ) ∈ n−p−1 h=l−1 I h → τ ∈ Sd d (K)\Sd d (K) (p+l−1) .…”

Asymptotic Topology of Random Subcomplexes in a Finite Simplicial Complex

“…Theorem 4 has the following quite surprising corollary which has already been observed by T. Akita [1] with a different (non-probabilistic) method, but also follows from the symmetry property observed by I.G. Macdonald [9], see [11].…”

The $e$-vector of a simplicial complex

“…Example: Let ∆ be the boundary of the tetrahedron. This complex has fvector (1,4,6,4), e-vector (−1, 4, −6, 4) and h-vector (1, 1, 1, 1). We note a few things from this calculation.…”