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Polynomial functions on Young diagrams arising from bipartite graphs

Abstract : 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.
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Maciej Dolęga, Piotr Sniady. Polynomial functions on Young diagrams arising from bipartite graphs. 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.257-268. ⟨hal-01215109⟩

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