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Equivariant Hilbert
series for hierarchical Models
Aida Maraj and Uwe Nagel |
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Vol. 12 (2021), No. 1, 21–42
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Abstract |
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Toric ideals to hierarchical models are invariant under the action of a product of symmetric groups. Taking the number of factors, say, , into account, we introduce and study invariant filtrations and their equivariant Hilbert series. We present a condition that guarantees that the equivariant Hilbert series is a rational function in variables with rational coefficients. Furthermore we give explicit formulas for the rational functions with coefficients in a number field and an algorithm for determining the rational functions with rational coefficients. A key is to construct finite automata that recognize languages corresponding to invariant filtrations. |
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Keywords
hierarchical model, invariant filtration, equivariant
Hilbert series, finite automaton, regular language
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Mathematical Subject Classification 2010
Primary: 05A15, 13P25, 68W30
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Milestones
Received: 4 November 2019
Revised: 31 July 2020
Accepted: 31 August 2020
Published: 9 April 2021
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Authors |
| Aida Maraj | |
| Max Planck Institute for Mathematics
in the Sciences Leipzig Germany |
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| Uwe Nagel | |
| Department of Mathematics University of Kentucky Lexington, KY United States |
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