Geodesic
Littlewood-Richardson coefficients and integrable tilings
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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We provide direct proofs of product and coproduct formulae for Schur functions where the coefficients (Littlewood–Richardson coefficients) are defined as counting puzzles. The product formula includes a second alphabet for the Schur functions, allowing in particular to recover formulae of [Molev–Sagan '99] and [Knutson–Tao '03] for factorial Schur functions. The method is based on the quantum integrability of the underlying tiling model.
DOI : 10.37236/101
Classification : 05E05, 81R12 
@article{10_37236_101,
     author = {Paul Zinn-Justin},
     title = {Littlewood-Richardson coefficients and integrable tilings},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/101},
     zbl = {1184.05133},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/101/}
}
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Paul Zinn-Justin. Littlewood-Richardson coefficients and integrable tilings. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/101

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