NDLI: Minimal Paths between Maximal Chains in Finite Rank Semimodular Lattices

Content Provider	Springer Nature Link
Author	Herscovici, David Samuel
Copyright Year	1998
Abstract	We study paths between maximal chains, or “flags,” in finite rank semimodular lattices. Two flags are adjacent if they differ on at most one rank. A path is a sequence of flags in which consecutive flags are adjacent. We study the union of all flags on at least one minimum length path connecting two flags in the lattice. This is a subposet of the original lattice. If the lattice is modular, the subposet is equal to the sublattice generated by the flags. It is a distributive lattice which is determined by the “Jordan-Hölder permutation” between the flags. The minimal paths correspond to all reduced decompositions of this permutation. In a semimodular lattice, the subposet is not uniquely determined by the Jordan-Hölder permutation for the flags. However, it is a join sublattice of the distributive lattice corresponding to this permutation. It is semimodular, unlike the lattice generated by the two flags, which may not be ranked. The minimal paths correspond to some reduced decompositions of the permutation, though not necessarily all. We classify the possible lattices which can arise in this way, and characterize all possibilities for the set of shortest paths between two flags in a semimodular lattice.
Starting Page	17
Ending Page	37
Page Count	21
File Format	PDF
ISSN	09259899
Journal	Journal of Algebraic Combinatorics
Volume Number	7
Issue Number	1
e-ISSN	15729192
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	1998-01-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Computer Science Group Theory and Generalizations Order, Lattices, Ordered Algebraic Structures Combinatorics Convex and Discrete Geometry
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

Semimodular Lattices and Semibuildings

Algebraic curves and maximal arcs

A Weighted Enumeration of Maximal Chains in the Bruhat Order

Minimal length maximal green sequences and triangulations of polygons

Actions of Finite Hypergroups

Unitals in Finite Desarguesian Planes

Discrete Polymatroids

A combinatorial formula for rank 2 cluster variables

Orthogonal Matroids

Minimal Paths between Maximal Chains in Finite Rank Semimodular Lattices

Similar Documents

Semimodular Lattices and Semibuildings

Algebraic curves and maximal arcs

A Weighted Enumeration of Maximal Chains in the Bruhat Order

Minimal length maximal green sequences and triangulations of polygons

Actions of Finite Hypergroups

Unitals in Finite Desarguesian Planes

Discrete Polymatroids

A combinatorial formula for rank 2 cluster variables

Orthogonal Matroids

Minimal Paths between Maximal Chains in Finite Rank Semimodular Lattices