Polynomial functions on Young diagrams arising from bipartite graphs

Details Polynomial functions on Young diagrams arising from bipartite graphs Polynomial functions on Young diagrams arising from bipartite graphs

2011-05-13

arxiv.org/abs/1105.2703v1

Discrete Mathematics & Theoretical Computer Science Proc. AO, 2011, 257-268

Mathematics

Combinatorics

To appear in DMTCS proc

Scientific paper

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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