Vol. 3, No. 2, 2010

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 4, 547–726
Issue 3, 365–546
Issue 2, 183–364
Issue 1, 1–182

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Author Index
Coming Soon
 
Other MSP Journals
The Gram determinant for plane curves

Józef H. Przytycki and Xiaoqi Zhu

Vol. 3 (2010), No. 2, 149–169
Abstract

We investigate the Gram determinant of the pairing arising from curves in a planar surface, with a focus on the disk with two holes. We prove that the determinant based on n 1 curves divides the determinant based on n curves. Motivated by the work on Gram determinants based on curves in a disk and curves in an annulus (Temperley–Lieb algebra of type A and B, respectively), we calculate several examples of the Gram determinant based on curves in a disk with two holes, and advance conjectures on the complete factorization of Gram determinants.

Keywords
Gram determinants, planar curves, noncrossing partitions, chromatic joins, Temperley–Lieb
Mathematical Subject Classification 2000
Primary: 05A99, 57M99
Milestones
Received: 30 November 2008
Revised: 27 April 2010
Accepted: 3 June 2010
Published: 11 August 2010

Communicated by Kenneth S. Berenhaut
Authors
Józef H. Przytycki
Department of Mathematics
The George Washington University
Washington, DC 20052
United States
Xiaoqi Zhu
Department of Applied Mathematics
Harvard University
Cambridge, MA 02138
United States