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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).

Abstract

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.

Acknowledgments

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.

Citation

Download Citation

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

Information

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

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

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

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Vol.58 • No. 3 • July 2021
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