Pith. sign in

REVIEW 2 cited by

Bialgebras in cointeraction, the antipode and the eulerian idempotent

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2201.11974 v5 pith:7WTNZZFK submitted 2022-01-28 math.RA

classification math.RA
keywords bialgebrasantipodedoubleeulerianidempotentpolynomialresultsaccent
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We give here a review of results about double bialgebras, that is to say bialgebras with two coproducts, the first one being a comodule morphism for the coaction induced by the second one. An accent is put on the case of connected bialgebras. The subjects of these results are the monoid of characters and their actions, polynomial invariants, the antipode and the eulerian idempotent. As examples, they are applied on a double bialgebra of graphs and on quasishuffle bialgebras. This includes a new proof of a combinatorial interpretation of the coefficients of the chromatic polynomial due to Greene and Zaslavsky.

Discussion (0). Sign in to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. An equality for balanced digraphs

    math.CO 2025-07 accept novelty 7.0 of 10

    The number of k-arc acyclic subdigraphs in which every vertex can reach a fixed root is independent of the root, for any balanced digraph.

  2. Extended generalized permutahedra, and cointeracting bialgebras

    math.RA 2026-07 accept novelty 6.5 of 10

    EGPs and affine-cone EGPs form cointeracting bimonoids in species measured by the monoid of EGPs, via the face-and-tangent-cone map, with explicit submodular functions for faces and cones.

Pith tools