scholarly journals Lower bounds for Betti numbers of special extensions

2005 ◽  
Vol 201 (1-3) ◽  
pp. 328-339
Author(s):  
Melvin Hochster ◽  
Benjamin Richert
Keyword(s):  
Lower Bounds ◽  
Betti Numbers

Lower Bounds for Arithmetic Networks II: Sum of Betti Numbers

1995 ◽  
Vol 7 (1) ◽  
pp. 41 ◽  
Author(s):  
J. L. Montaña ◽  
J. E. Morais ◽  
Luis M. Pardo
Keyword(s):  
Lower Bounds ◽  
Betti Numbers ◽  
Arithmetic Networks

scholarly journals Average Betti Numbers of Induced Subcomplexes in Triangulations of Manifolds

10.37236/8564 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Giulia Codenotti ◽  
Jonathan Spreer ◽  
Francisco Santos
Keyword(s):  
Simplicial Complex ◽  
Lower Bounds ◽  
Commutative Algebra ◽  
Betti Numbers ◽  
Upper Bounds ◽  
Weighted Sums ◽  
Weighted Averages ◽  
Connected Sums ◽  
Graded Betti Numbers ◽  
Strongly Connected

We study a variation of Bagchi and Datta's $\sigma$-vector of a simplicial complex $C$, whose entries are defined as weighted averages of Betti numbers of induced subcomplexes of $C$. We show that these invariants satisfy an Alexander-Dehn-Sommerville type identity, and behave nicely under natural operations on triangulated manifolds and spheres such as connected sums and bistellar flips. In the language of commutative algebra, the invariants are weighted sums of graded Betti numbers of the Stanley-Reisner ring of $C$. This interpretation implies, by a result of Adiprasito, that the Billera-Lee sphere maximizes these invariants among triangulated spheres with a given $f$-vector. For the first entry of $\sigma$, we extend this bound to the class of strongly connected pure complexes. As an application, we show how upper bounds on $\sigma$ can be used to obtain lower bounds on the $f$-vector of triangulated $4$-manifolds with transitive symmetry on vertices and prescribed vector of Betti numbers.

scholarly journals Lower bounds for Betti numbers of monomial ideals

2018 ◽  
Vol 508 ◽  
pp. 445-460 ◽  
Author(s):  
Adam Boocher ◽  
James Seiner
Keyword(s):  
Lower Bounds ◽  
Betti Numbers ◽  
Monomial Ideals

Lower bounds for arithmetic networks II: Sum of Betti numbers

1996 ◽  
Vol 7 (1) ◽  
pp. 41-51 ◽  
Author(s):  
J. L. Montaña ◽  
J. E. Morais ◽  
Luis M. Pardo
Keyword(s):  
Lower Bounds ◽  
Betti Numbers ◽  
Arithmetic Networks

scholarly journals On the Betti Numbers of some Classes of Binomial Edge Ideals

10.37236/3689 ◽  
2013 ◽  
Vol 20 (4) ◽  
Author(s):  
Sohail Zafar ◽  
Zohaib Zahid
Keyword(s):  
Lower Bounds ◽  
Betti Numbers ◽  
Edge Ideal ◽  
Induced Subgraphs ◽  
Edge Ideals ◽  
Arbitrary Graphs

We study the Betti numbers of binomial edge ideal associated to some classes of graphs with large Castelnuovo-Mumford regularity. As an application we give several lower bounds of the Castelnuovo-Mumford regularity of arbitrary graphs depending on induced subgraphs.

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base
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