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A Quantization of a theorem of Goulden and Jackson

Abstract : A theorem of Goulden and Jackson which gives interesting formulae for character immanants also implies MacMahon's Master Theorem. We quantize Goulden and Jackson's theorem to give formulae for quantum character immanants in such a way as to obtain a known quantization of MacMahon's Master Theorem due to Garoufalidis-Lê-Zeilberger. In doing so, we also quantize formulae of Littlewood, Merris and Watkins concerning induced character immanants.
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Matjaž Konvalinka, Mark Skandera. A Quantization of a theorem of Goulden and Jackson. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.369-380. ⟨hal-01185156⟩

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