Issue
EPL
Volume 86, Number 3, May 2009
Article Number 33001
Number of page(s) 4
Section Atomic, Molecular and Optical Physics
DOI http://dx.doi.org/10.1209/0295-5075/86/33001
Published online 15 May 2009
EPL, 86 (2009) 33001
DOI: 10.1209/0295-5075/86/33001

Counting paths in Bratteli diagrams for SU(2)k

T. Mansour1 and S. Severini2

1   Department of Mathematics, University of Haifa - Haifa 31905, Israel
2   Institute for Quantum Computing and Department of Combinatorics & Optimization, University of Waterloo Waterloo N2L 3G1, Canada

simoseve@gmail.com

received 30 January 2009; accepted in final form 9 April 2009; published May 2009
published online 15 May 2009

Abstract
It is known that the Hilbert space dimensionality for quasiparticles in an SU(2)k Chern-Simons-Witten theory is given by a number of directed paths in certain Bratteli diagrams. We present an explicit formula for these numbers for arbitrary k. This is on the basis of a relation with Dyck paths and Chebyshev polynomials.

PACS
31.15.xm - Quasiparticle methods.
02.10.Ox - Combinatorics; graph theory.

© EPLA 2009