Geodesic
The Hopf monoid on nonnesting supercharacters of pattern groups
Journal of Algebraic Combinatorics, Tome 42 (2015) no. 1, pp. 129-164.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 20C15, 20C33, 05E10, 20G05, 20G40
Keywords: supercharacter, unipotent group, Hopf monoid 
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     author = {Andrews, Scott},
     title = {The {Hopf} monoid on nonnesting supercharacters of pattern groups},
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     url = {http://geodesic.mathdoc.fr/item/JAC_2015__42_1_a6/}
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Andrews, Scott. The Hopf monoid on nonnesting supercharacters of pattern groups. Journal of Algebraic Combinatorics, Tome 42 (2015) no. 1, pp. 129-164. http://geodesic.mathdoc.fr/item/JAC_2015__42_1_a6/