| Issue |
EPL
Volume 86, Number 3, May 2009
|
|
|---|---|---|
| Article Number | 33001 | |
| Number of page(s) | 4 | |
| Section | Atomic, Molecular and Optical Physics | |
| DOI | https://doi.org/10.1209/0295-5075/86/33001 | |
| Published online | 15 May 2009 | |
Counting paths in Bratteli diagrams for SU(2)k
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
Corresponding author: simoseve@gmail.com
Received:
30
January
2009
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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