Abstract
In this chapter, we investigate the algebra of polynomial functions in coordinates of Young diagrams as a nice framework in which various quantities on Young diagrams can be efficiently computed. This algebra was introduced by Kerov–Olshanski [20], analysis of which is substantially due to Ivanov–Olshanski [16]. Several systems of generators and associated generating functions are considered. It is important to understand the concrete transition rules between these generating systems, one of which is the Kerov polynomial.
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The argument follows Proposition 1.5 in [16].
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Hora, A. (2016). Analysis of the Kerov–Olshanski Algebra. In: The Limit Shape Problem for Ensembles of Young Diagrams. SpringerBriefs in Mathematical Physics, vol 17. Springer, Tokyo. https://doi.org/10.1007/978-4-431-56487-4_2
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DOI: https://doi.org/10.1007/978-4-431-56487-4_2
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Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-56485-0
Online ISBN: 978-4-431-56487-4
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