NDLI: K-Eulerian Posets

Content Provider	Springer Nature Link
Author	Ehrenborg, Richard
Copyright Year	2001
Abstract	A poset P is called k-Eulerian if every interval of rank k is Eulerian. The class of k-Eulerian posets interpolates between graded posets and Eulerian posets. It is a straightforward observation that a 2k-Eulerian poset is also (2k+1)-Eulerian. We prove that the ab-index of a (2k+1)-Eulerian poset can be expressed in terms of c=a+b, d=ab+ba and e $^{2k+1}$=(a−b)$^{2k+1}$. The proof relies upon the algebraic approaches of Billera-Liu and Ehrenborg-Readdy. We extend the Billera-Liu flag algebra to a Newtonian coalgebra. This flag Newtonian coalgebra forms a Laplace pairing with the Newtonian coalgebra k〈a,b〉 studied by Ehrenborg-Readdy. The ideal of flag operators that vanish on (2k+1)-Eulerian posets is also a coideal. Hence, the Laplace pairing implies that the dual of the coideal is the desired subalgebra of k〈a,b〉. As a corollary we obtain a proof of the existence of the cd-index which does not use induction.
Starting Page	227
Ending Page	236
Page Count	10
File Format	PDF
ISSN	01678094
Journal	Order
Volume Number	18
Issue Number	3
e-ISSN	15729273
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2001-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theory of Computation Geometry Convex and Discrete Geometry
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Computational Theory and Mathematics Geometry and Topology

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

K-Eulerian Posets