Volume 86, Number 3, May 2009
|Number of page(s)||4|
|Section||Atomic, Molecular and Optical Physics|
|Published online||15 May 2009|
Counting paths in Bratteli diagrams for SU(2)k
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
Corresponding author: firstname.lastname@example.org
Accepted: 9 April 2009
It is known that the Hilbert space dimensionality for quasiparticles in an 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
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