The r-signed Birkhoff transform

Richard Ehrenborg

doi:10.1016/j.disc.2020.112214

The r-signed Birkhoff transform

Richard Ehrenborg

Mathematics

Producción científica: Article › revisión exhaustiva

2 Citas (Scopus)

Resumen

We introduce the r-signed Birkhoff transform of a distributive lattice, extending Hsiao's notion of the signed Birkhoff transform. We show how to compute the ab-index of the r-signed Birkhoff transform from the ab-index of the distributive lattice, generalizing work of Billera, Ehrenborg and Readdy, by extending their ω map to ω_r. We also obtain new expressions for the ab-index of the r-cubical lattice in terms of the map ω_r applied to all the permutations in the symmetric group. We show that the map r⋅ω_r=ϑ_r is an endomorphism on the Hopf algebra of quasisymmetric functions.

Idioma original	English
Número de artículo	112214
Publicación	Discrete Mathematics
Volumen	344
N.º	2
DOI	https://doi.org/10.1016/j.disc.2020.112214
Estado	Published - feb 2021

Nota bibliográfica

Publisher Copyright:
© 2020 Elsevier B.V.

Financiación

The author thanks the referee for comments that lead to an improved exposition in this paper. The author thanks Margaret Readdy and Vic Reiner for discussions about complex polytopes. The author also thanks Margaret Readdy for helpful comments on an earlier version of this paper. The author also thanks the Institute for Advanced Study for a research visit 2019. The author was partially supported by National Science Foundation, United States of America grant 0200624 . This work was partially supported by a grant from the Simons Foundation, United States of America ( #429370 to Richard Ehrenborg).

Financiadores	Número del financiador
Simons Foundation
Institute for Advanced Study
National Science Foundation Arctic Social Science Program	0200624
Arup Limited, United States of America	429370

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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ER -

The r-signed Birkhoff transform

Resumen

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ASJC Scopus subject areas

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