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On a Theorem of Baxter and Zeilberger via a Result of Roselle

Abstract

We provide a new proof of a result of Baxter and Zeilberger showing that \({{\,\mathrm{inv}\,}}\) and \({{\,\mathrm{maj}\,}}\) on permutations are jointly independently asymptotically normally distributed. The main feature of our argument is that it uses a generating function due to Roselle, answering a question raised by Romik and Zeilberger.

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Acknowledgements

The author would like to thank Dan Romik and Doron Zeilberger for providing the impetus for the present work and feedback on the manuscript. He would also like to thank Sara Billey and Matjaž Konvalinka for valuable discussion on related work, and he gratefully acknowledges Sara Billey for her very careful reading of the manuscript and many helpful suggestions. Finally, thanks also go to the anonymous referees for their careful reading of the manuscript and useful suggestions.

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Correspondence to Joshua P. Swanson.

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Communicated by Eric Fusy.

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Swanson, J.P. On a Theorem of Baxter and Zeilberger via a Result of Roselle. Ann. Comb. 26, 87–95 (2022). https://doi.org/10.1007/s00026-022-00570-x

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  • DOI: https://doi.org/10.1007/s00026-022-00570-x