Geodesic
Polynomial functions on Young diagrams arising from bipartite graphs
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011).

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We study the class of functions on the set of (generalized) Young diagrams arising as the number of embeddings of bipartite graphs. We give a criterion for checking when such a function is a polynomial function on Young diagrams (in the sense of Kerov and Olshanski) in terms of combinatorial properties of the corresponding bipartite graphs. Our method involves development of a differential calculus of functions on the set of generalized Young diagrams. 
@article{DMTCS_2011_special_260_a21,
     author = {Dol\k{e}ga, Maciej and Sniady, Piotr},
     title = {Polynomial functions on {Young} diagrams arising from bipartite graphs},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)},
     year = {2011},
     doi = {10.46298/dmtcs.2908},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2908/}
}
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%D 2011
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Dolęga, Maciej; Sniady, Piotr. Polynomial functions on Young diagrams arising from bipartite graphs. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011). doi : 10.46298/dmtcs.2908. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2908/

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