Abstract

Toric ideals to hierarchical models are invariant under the action of a product of symmetric groups. Taking the number of factors, say, $m$, 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 $m+1$ 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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Mathematical Subject Classification 2010

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