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A simplicial groupoid for plethysm

Alex Cebrian
Algebraic & Geometric Topology 21 (2021) 421–445
DOI: 10.2140/agt.2021.21.421
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
References
Publication
Received: 17 September 2019
Revised: 3 May 2020
Accepted: 19 May 2020
Published: 25 February 2021
Authors
Alex Cebrian
Departament de Matemàtiques
Universitat Autònoma de Barcelona
Cerdanyola del Vallès
Spain
http://mat.uab.cat/~acebrian/