NDLI: Simplicial orders and chordality

Content Provider	Springer Nature Link
Author	Bigdeli, Mina Herzog, Jürgen Yazdan Pour, Ali Akbar Zaare Nahandi, Rashid
Copyright Year	2016
Abstract	Chordal clutters in the sense of Bigdeli et al. (J Comb Theory Ser A 145:129–149, 2017) and Morales et al. (Ann Fac Sci Toulouse Sér 6 23(4):877–891, 2014) are defined via simplicial orders. Their circuit ideal has a linear resolution, independent of the characteristic of the base field. We show that any Betti sequence of an ideal with linear resolution appears as the Betti sequence of the circuit ideal of such a chordal clutter. Associated with any simplicial order is a sequence of integers which we call the $$\lambda $$ -sequence of the chordal clutter. All possible $$\lambda $$ -sequences are characterized. They are intimately related to the Hilbert function of a suitable standard graded K-algebra attached to the chordal clutter. By the $$\lambda $$ -sequence of a chordal clutter, we determine other numerical invariants of the circuit ideal, such as the $$\mathbf h $$ -vector and the Betti numbers.
Ending Page	1039
Page Count	19
Starting Page	1021
File Format	PDF
ISSN	09259899
e-ISSN	15729192
Journal	Journal of Algebraic Combinatorics
Issue Number	4
Volume Number	45
Language	English
Publisher	Springer US
Publisher Date	2016-12-19
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Combinatorial aspects of simplicial complexes Computational homological algebra Betti number Convex and Discrete Geometry Simplicial order Syzygies, resolutions, complexes Computer Science Hilbert function Order, Lattices, Ordered Algebraic Structures Group Theory and Generalizations Chordal clutter Hypergraphs Combinatorics $$\lambda $$ -sequence
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Stanley depth and simplicial spanning trees

Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers

Algebraic properties of ideals of poset homomorphisms

Generalized splines and graphic arrangements

Resolutions of letterplace ideals of posets

Betti numbers of lex ideals over some Macaulay-Lex rings

Spectral Sequences on Combinatorial Simplicial Complexes

Finite Free Resolutions and 1-Skeletons of Simplicial Complexes

Divisors on graphs, orientations, syzygies, and system reliability

Simplicial orders and chordality

Similar Documents

Stanley depth and simplicial spanning trees

Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers

Algebraic properties of ideals of poset homomorphisms

Generalized splines and graphic arrangements

Resolutions of letterplace ideals of posets

Betti numbers of lex ideals over some Macaulay-Lex rings

Spectral Sequences on Combinatorial Simplicial Complexes

Finite Free Resolutions and 1-Skeletons of Simplicial Complexes

Divisors on graphs, orientations, syzygies, and system reliability

Simplicial orders and chordality