Betti numbers
The Betti numbers of forests
... Abstract. This paper produces a recursive formula of the Betti numbers of certain Stanley- Reisner ideals (graph ideals associated to forests). This gives a purely combinatorial definition of the projective ...
13
Characteristic-independence of Betti numbers of graph ideals
... One of the central problems in Commutative Algebra is the description of minimal resolutions of ideals. Even when one restricts one’s attention to ideals of polynomial rings generated by monomials, the structure of the ...
19
Free minimal resolutions and the Betti numbers of the suspension of an n gon
... Abstract. Consider the general n-gon with vertices at the points 1, 2,...,n. Then its sus- pension involves two more vertices, say at n +1 and n+ 2. Let R be the polynomial ring k[x 1 ,x 2 ,...,x n ], where k is any ...
6
On The Total Curvature And Betti Numbers Of Complex Projective Manifolds
... between the degrees of real algebraic varieties and their Betti numbers. Based on their comments, both authors seem to have considered the possibility of extending their results using some of the ...
80
Pascal type properties of Betti numbers
... Betti numbers, finite abstract simplicial complex, StanleyReisner ideal, free minimal resolutions, Koszul complex, double complex.. 1991 AMS SUBJECT CLASSIFICATION CODE.[r] ...
8
A Simple Proof of the Formula for the Betti Numbers of the Quasihomogeneous Hilbert Schemes
... In [4], as a corollary of Theorem 1.1, there was derived a combinatorial identity. In the same way Theorem 1.2 leads to a more general combinatorial identity. Denote by Y the set of all Young diagrams. The number of ...
7
Bouchat
... graded Betti numbers by listing all depth sequence created from a string of n ones using operations O1 and O2, separating these sequences into their fundamental subsequences, enumerating each subsequence ...
12
Mohamed El Naschie’s Revision of Albert Einstein’s E = m0c2: A Definite Resolution of the Mystery of the Missing Dark Energy of the Cosmos
... two Betti numbers [9-12] fixes the homology of space-time’s de Rham to- pology of smooth classical space-time of relativity and the rugged K3 Kähler [11] based quantum space-time of quantum gravity and give ...
5
On The Torsion Homology of Non-Arithmetic Hyperbolic Tetrahedral Groups
... then the limit (1) tends to 1/(6π). In the case of positive first Betti numbers, the ratios “log(torsion)/volume” get much smaller than 1/(6π). These observations support the general philosophy of Bergeron ...
10
Multi criteria adaptation mechanisms in homological sensor networks
... First, the base station node has to calculate H0 R and H1 R to make sure the betti numbers are 1 and 0 respectively, which means currently all sensor nodes provide a connected communicat[r] ...
6
Comparing the Morse index and the first Betti number of minimal hypersurfaces
... Savo’s work was preceded by the work of Ros (see [29] and refer- ences therein for partially similar contributions). Considering flat three dimensional tori, Ros observed that, when a harmonic one-form on a closed ...
32
On the torsion homology of non-arithmetic hyperbolic tetrahedral groups
... In the case of positive first Betti numbers, the ratios “log(torsion)/volume” get much smaller than 1/(6π). These observations support the general philosophy of Bergeron and Venkatesh as discussed in ...
11
Bouchat
... multi-graded Betti numbers for path ideals of rooted ...the Betti numbers corresponding to a path ideal of a rooted tree will also provide a method to compute the projective dimension as well ...
13
Salt Tectonism In The Carolina Trough
... A ring that meets this upper-bound is called a Golod ring, named for Evgenii Golod who first examined such rings in [4]. This upper-bound is a rational function in t since both P k k k S (t) and P R S (t) are ...
49
Descent Systems, Eulerian Polynomials and Toric Varieties
... permutahedron. The Betti numbers of X(∅) are given by the Eulerian numbers. In [4], Brenti studies the descent polynomials (i.e., the Poincar´e polynomials of X(∅)) as analogues of the Eulerian ...
126
Kähler Dark Matter, Dark Energy Cosmic Density and Their Coupling
... various Betti numbers can discriminate between not only ordinary and dark energy but also between dark matter and pure dark ...non-zero Betti numbers [24] ...
11
Search | Preprints
... the Betti numbers of the corresponding directed flag complex (as was done, using a much larger spiking dataset and without an attempt at classification, in [13]), and observe that using tournaplexes with ...
19
Geometry and Topology of the Boolean Model on a Stationary Point Processes : A Brief Survey
... are Betti numbers k (C( n ; r)); k = 0, ...persistent Betti numbers k (C( n ; r, s)); k = 0, ...persistent Betti numbers are rather meant to count the ‘holes’ or non- ...
10
(n 2) tightness and curvature of submanifolds with boundary
... The following results give certain connections between n-2-tightness on one hand and usual curvature terms and the sum of the Betti-numbers on the other.. Note that in case.[r] ...
11
Seeing Numbers
... their numbers and later, back at home, he consulted a book of numerical tables and what he found was that all the six-figure numbers were primes! The next day he dared to surprise the twins and ventured his ...
16