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arXiv · 1010.4072

Codes and shifted codes of partitions

J. T. Hird·Naihuan Jing·Ernest Stitzinger
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Abstract

In a recent paper, Carrell and Goulden found a combinatorial identity of the Bernstein operators that they then used to prove Bernstein's Theorem. We show that this identity is a straightforward consequence of the classical result. We also show how a similar approach using the codes of partitions can be generalized from Schur functions to also include Schur $Q$-functions and derive the combinatorial formulation for both cases. We then apply them by examining the Littlewood-Richardson and Pieri Rules.

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J. T. Hird, Naihuan Jing, Ernest Stitzinger. 2010-10-19. Codes and shifted codes of partitions. https://doi.org/10.1142/s0218196711006595

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