scholarly journals Combinatorics of Symbolic Rees Algebras of Edge Ideals of Clutters

2015 ◽  
pp. 537-566
Keyword(s):  
Edge Ideals ◽  
Rees Algebras

scholarly journals Almost complete intersection binomial edge ideals and their Rees algebras

2021 ◽  
Vol 225 (6) ◽  
pp. 106628 ◽  
Author(s):  
A.V. Jayanthan ◽  
Arvind Kumar ◽  
Rajib Sarkar
Keyword(s):  
Complete Intersection ◽  
Edge Ideals ◽  
Rees Algebras

Rees algebras of edge ideals

1995 ◽  
Vol 23 (9) ◽  
pp. 3513-3524 ◽  
Author(s):  
Rafael H. Villarreal
Keyword(s):  
Edge Ideals ◽  
Rees Algebras

scholarly journals Blow-up algebras, determinantal ideals, and Dedekind–Mertens-like formulas

2017 ◽  
Vol 29 (4) ◽  
Author(s):  
Alberto Corso ◽  
Uwe Nagel ◽  
Sonja Petrović ◽  
Cornelia Yuen
Keyword(s):  
Blow Up ◽  
Symmetric Matrix ◽  
Monomial Ideals ◽  
Edge Ideals ◽  
Rees Algebras ◽  
Determinantal Ideals ◽  
Blowing Up ◽  
Initial Ideals ◽  
Vertex Decomposable ◽  
Liaison Theory

AbstractWe investigate Rees algebras and special fiber rings obtained by blowing up specialized Ferrers ideals. This class of monomial ideals includes strongly stable monomial ideals generated in degree two and edge ideals of prominent classes of graphs. We identify the equations of these blow-up algebras. They generate determinantal ideals associated to subregions of a generic symmetric matrix, which may have holes. Exhibiting Gröbner bases for these ideals and using methods from Gorenstein liaison theory, we show that these determinantal rings are normal Cohen–Macaulay domains that are Koszul, that the initial ideals correspond to vertex decomposable simplicial complexes, and we determine their Hilbert functions and Castelnuovo–Mumford regularities. As a consequence, we find explicit minimal reductions for all Ferrers and many specialized Ferrers ideals, as well as their reduction numbers. These results can be viewed as extensions of the classical Dedekind–Mertens formula for the content of the product of two polynomials.

scholarly journals Combinatorics of symbolic Rees algebras of edge ideals of clutters

2011 ◽  
pp. 151-164 ◽  
Author(s):  
José Martínez-Bernal ◽  
Carlos Rentería-Márquez ◽  
Rafael Villarreal
Keyword(s):  
Edge Ideals ◽  
Rees Algebras

scholarly journals A proof for a conjecture on the regularity of binomial edge ideals

2021 ◽  
Vol 180 ◽  
pp. 105432
Author(s):  
Mohammad Rouzbahani Malayeri ◽  
Sara Saeedi Madani ◽  
Dariush Kiani
Keyword(s):  
Edge Ideals

scholarly journals On vanishing patterns in j-strands of edge ideals

2017 ◽  
Vol 46 (2) ◽  
pp. 287-295 ◽  
Author(s):  
Abed Abedelfatah ◽  
Eran Nevo
Keyword(s):  
Edge Ideals

scholarly journals Sequentially Cohen–Macaulay Rees algebras

2017 ◽  
Vol 69 (1) ◽  
pp. 293-309
Author(s):  
Naoki TANIGUCHI ◽  
Tran Thi PHUONG ◽  
Nguyen Thi DUNG ◽  
Tran Nguyen AN
Keyword(s):  
Rees Algebras

scholarly journals Stanley depth of edge ideals

2012 ◽  
Vol 49 (4) ◽  
pp. 501-508 ◽  
Author(s):  
Muhammad Ishaq ◽  
Muhammad Qureshi
Keyword(s):  
Complete Graph ◽  
Upper Bound ◽  
Edge Ideal ◽  
Stanley Depth ◽  
Edge Ideals

We give an upper bound for the Stanley depth of the edge ideal I of a k-partite complete graph and show that Stanley’s conjecture holds for I. Also we give an upper bound for the Stanley depth of the edge ideal of a s-uniform complete bipartite hypergraph.

scholarly journals Gorenstein binomial edge ideals

2021 ◽  
Author(s):  
René González‐Martínez
Keyword(s):  
Edge Ideals
Sign in / Sign up

Export Citation Format

Share Document