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The Hopf monoid on nonnesting supercharacters of pattern groups

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Abstract

We construct supercharacter theories for a collection of unipotent matrix groups and produce a Hopf monoid from the supercharacters. These supercharacter theories are coarser than those defined by Diaconis–Isaacs for algebra groups and have supercharacters and superclasses indexed by nonnesting-labeled set partitions. We compute the supercharacter tables and describe the product and coproduct of the Hopf monoid combinatorially. We also show that this Hopf monoid is free.

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Acknowledgments

I would like to thank Nat Thiem for his numerous helpful suggestions and insights. Many thanks as well to the referees, whose remarks and clarifications were greatly appreciated.

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  1. Department of Mathematics, University of Colorado Boulder, Boulder, CO, 80309, USA

    Scott Andrews

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  1. Scott Andrews
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Andrews, S. The Hopf monoid on nonnesting supercharacters of pattern groups. J Algebr Comb 42, 129–164 (2015). https://doi.org/10.1007/s10801-014-0576-8

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  • DOI: https://doi.org/10.1007/s10801-014-0576-8

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