Geodesic
The Geometry of Lecture Hall Partitions and Quadratic Permutation Statistics
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010).

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We take a geometric view of lecture hall partitions and anti-lecture hall compositions in order to settle some open questions about their enumeration. In the process, we discover an intrinsic connection between these families of partitions and certain quadratic permutation statistics. We define some unusual quadratic permutation statistics and derive results about their joint distributions with linear statistics. We show that certain specializations are equivalent to the lecture hall and anti-lecture hall theorems and another leads back to a special case of a Weyl group generating function that "ought to be better known.'' 
@article{DMTCS_2010_special_259_a70,
     author = {Bright, Katie L. and Savage, Carla D.},
     title = {The {Geometry} of {Lecture} {Hall} {Partitions} and {Quadratic} {Permutation} {Statistics}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)},
     year = {2010},
     doi = {10.46298/dmtcs.2875},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2875/}
}
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Bright, Katie L.; Savage, Carla D. The Geometry of Lecture Hall Partitions and Quadratic Permutation Statistics. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010). doi : 10.46298/dmtcs.2875. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2875/

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