On vanishing patterns in j-strands of edge ideals

Abed Abedelfatah; Eran Nevo

doi:10.1007/s10801-017-0747-5

On vanishing patterns in j-strands of edge ideals

Abed Abedelfatah^*, Eran Nevo

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We consider two problems regarding vanishing patterns in the Betti table of edge ideals I over any fixed field. First, we show that the j-strand is connected if j= 3 (for j= 2 this is easy and known), and give examples where the j-strand is not connected for any j> 3. Next, we apply our result on strand connectivity to establish the subadditivity conjecture for edge ideals, t_a ₊ _b(I) ≤ t_a(I) + t_b(I) , in case b= 2 , 3 (the case b= 1 is known). Here t_i(I) denote the maximal shifts in the minimal free resolution of S / I over its polynomial algebra.

Original language	English
Pages (from-to)	287-295
Number of pages	9
Journal	Journal of Algebraic Combinatorics
Volume	46
Issue number	2
DOIs	https://doi.org/10.1007/s10801-017-0747-5
State	Published - 1 Sep 2017

Bibliographical note

Publisher Copyright:
© 2017, Springer Science+Business Media New York.

Keywords

Betti diagram
Edge ideal
Monomial ideal
Simplicial complex
Subadditivity

Access to Document

10.1007/s10801-017-0747-5

Cite this

@article{5f8d6f003fac4d9780d3b582519f334d,

title = "On vanishing patterns in j-strands of edge ideals",

abstract = "We consider two problems regarding vanishing patterns in the Betti table of edge ideals I over any fixed field. First, we show that the j-strand is connected if j= 3 (for j= 2 this is easy and known), and give examples where the j-strand is not connected for any j> 3. Next, we apply our result on strand connectivity to establish the subadditivity conjecture for edge ideals, ta + b(I) ≤ ta(I) + tb(I) , in case b= 2 , 3 (the case b= 1 is known). Here ti(I) denote the maximal shifts in the minimal free resolution of S / I over its polynomial algebra.",

keywords = "Betti diagram, Edge ideal, Monomial ideal, Simplicial complex, Subadditivity",

author = "Abed Abedelfatah and Eran Nevo",

note = "Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media New York.",

year = "2017",

month = sep,

day = "1",

doi = "10.1007/s10801-017-0747-5",

language = "אנגלית",

volume = "46",

pages = "287--295",

journal = "Journal of Algebraic Combinatorics",

issn = "0925-9899",

publisher = "Springer Netherlands",

number = "2",

}

TY - JOUR

T1 - On vanishing patterns in j-strands of edge ideals

AU - Abedelfatah, Abed

AU - Nevo, Eran

PY - 2017/9/1

Y1 - 2017/9/1

N2 - We consider two problems regarding vanishing patterns in the Betti table of edge ideals I over any fixed field. First, we show that the j-strand is connected if j= 3 (for j= 2 this is easy and known), and give examples where the j-strand is not connected for any j> 3. Next, we apply our result on strand connectivity to establish the subadditivity conjecture for edge ideals, ta + b(I) ≤ ta(I) + tb(I) , in case b= 2 , 3 (the case b= 1 is known). Here ti(I) denote the maximal shifts in the minimal free resolution of S / I over its polynomial algebra.

AB - We consider two problems regarding vanishing patterns in the Betti table of edge ideals I over any fixed field. First, we show that the j-strand is connected if j= 3 (for j= 2 this is easy and known), and give examples where the j-strand is not connected for any j> 3. Next, we apply our result on strand connectivity to establish the subadditivity conjecture for edge ideals, ta + b(I) ≤ ta(I) + tb(I) , in case b= 2 , 3 (the case b= 1 is known). Here ti(I) denote the maximal shifts in the minimal free resolution of S / I over its polynomial algebra.

KW - Betti diagram

KW - Edge ideal

KW - Monomial ideal

KW - Simplicial complex

KW - Subadditivity

UR - http://www.scopus.com/inward/record.url?scp=85014621541&partnerID=8YFLogxK

U2 - 10.1007/s10801-017-0747-5

DO - 10.1007/s10801-017-0747-5

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85014621541

SN - 0925-9899

VL - 46

SP - 287

EP - 295

JO - Journal of Algebraic Combinatorics

JF - Journal of Algebraic Combinatorics

IS - 2

ER -

On vanishing patterns in j-strands of edge ideals

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this