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Hilbert series in the category of trees with contractions

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Abstract

We consider Hilbert series associated to modules over various categories of trees. Using the technology of Sam and Snowden (J Am Math Soc 30(1): 159–203, 2017) we show that these Hilbert series must be algebraic. We then apply these technical theorems to prove facts about certain natural generating functions associated to trees.

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Acknowledgements

The author was supported by NSF grant DMS-1704811. He would like to send thanks to Ben Young for various conversations that were useful during the creation of this work. He would also like to send thanks to Nick Proudfoot, whose editorial suggestions vastly improved the quality of the writing. Finally, the author would like to send thanks to the anonymous referee, whose suggestions greatly helped the clarity of certain arguments.

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  1. Department of Mathematics, University of Oregon, Eugene, OR, 97403, USA

    Eric Ramos

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  1. Eric Ramos
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Correspondence to Eric Ramos.

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Ramos, E. Hilbert series in the category of trees with contractions. Math. Z. 298, 1831–1852 (2021). https://doi.org/10.1007/s00209-020-02690-7

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