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Abstract
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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
and the Quillen
–construction.
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Keywords
plethysm, simplicial groupoids, incidence bialgebras
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Mathematical Subject Classification 2010
Primary: 05A18, 13F25, 16T10, 18B40, 18G30
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Publication
Received: 17 September 2019
Revised: 3 May 2020
Accepted: 19 May 2020
Published: 25 February 2021
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