Geodesic
Fully packed loop configurations : polynomiality and nested arches
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020).

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This extended abstract proves that the number of fully packed loop configurations whose link pattern consists of two noncrossing matchings separated by m nested arches is a polynomial in m. This was conjectured by Zuber (2004) and for large values of m proved by Caselli et al. (2004) 
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     author = {Aigner, Florian},
     title = {Fully packed loop configurations : polynomiality and nested arches},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
     year = {2020},
     doi = {10.46298/dmtcs.6341},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6341/}
}
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Aigner, Florian. Fully packed loop configurations : polynomiality and nested arches. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020). doi : 10.46298/dmtcs.6341. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6341/

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