Volume 21, issue 1 (2021)

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A simplicial groupoid for plethysm

Alex Cebrian

Algebraic & Geometric Topology 21 (2021) 421–445
Abstract

We give a simple combinatorial model for plethysm. Precisely, the bialgebra dual to plethystic substitution is realized as the homotopy cardinality of the incidence bialgebra of an explicit simplicial groupoid, obtained from surjections by a construction reminiscent of the Waldhausen $S$ and the Quillen $Q$–construction.

Keywords
plethysm, simplicial groupoids, incidence bialgebras
Mathematical Subject Classification 2010
Primary: 05A18, 13F25, 16T10, 18B40, 18G30