Geodesic
Singularity analysis via the iterated kernel method
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013).

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We provide exact and asymptotic counting formulas for five singular lattice path models in the quarter plane. Furthermore, we prove that these models have a non D-finite generating function. 
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     author = {Melczer, Stephen and Mishna, Marni},
     title = {Singularity analysis via the iterated kernel method},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)},
     year = {2013},
     doi = {10.46298/dmtcs.2317},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2317/}
}
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%A Mishna, Marni
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%V DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
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Melczer, Stephen; Mishna, Marni. Singularity analysis via the iterated kernel method. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013). doi : 10.46298/dmtcs.2317. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2317/

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