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July 2021 The Hopf monoid and the basic invariant of directed graphs
Keiju Kato
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Osaka J. Math. 58(3): 591-608 (July 2021).


Aguiar and Ardila defined the Hopf monoid ${\rm GP}$ of generalized permutahedra and showed that it contains many submonoids that correspond to combinatorial objects. They also give a basic polynomial invariant of generalized permutahedra, which then specializes to submonoids. We define the Hopf monoid of directed graphs and show that it also embeds in ${\rm GP}$. The resulting basic invariant coincides with the strict chromatic polynomial of Awan and Bernardi.


I should like to express my gratitude to Tamás Kálmán for constant encouragement and much helpful advice. I should also like to thank Keita Nakagane for his useful comments and discussions.


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Keiju Kato. "The Hopf monoid and the basic invariant of directed graphs." Osaka J. Math. 58 (3) 591 - 608, July 2021.


Received: 9 August 2019; Revised: 31 March 2020; Published: July 2021
First available in Project Euclid: 20 July 2021

Primary: 05C15, 05C20‎, 05C31
Secondary: 05C21, 52B05

Rights: Copyright © 2021 Osaka University and Osaka City University, Departments of Mathematics


Vol.58 • No. 3 • July 2021
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