Abstract
We use Giraudo’s construction of combinatorial operads from monoids to offer a conceptual explanation of the origins of Hoffbeck’s path sequences of shuffle trees, and use it to define new monomial orders of shuffle trees. One such order is utilised to exhibit a quadratic Gröbner basis of the Poisson operad.
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Acknowledgements
The author is grateful to Anton Khoroshkin and Pedro Tamaroff for useful discussions during the preparation of this article, and to Murray Bremner who posed a question of finding a quadratic Gröbner basis for the Poisson operad.
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Communicated by Martin Markl.
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Dotsenko, V. Word operads and admissible orderings. Appl Categor Struct 28, 595–600 (2020). https://doi.org/10.1007/s10485-020-09591-0
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DOI: https://doi.org/10.1007/s10485-020-09591-0