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Algebraic Characterization of \({{\mathbb {C}}}\)-Regular Fractions Under Level Permutations

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Abstract

In this paper we study the behavior of the fractions of a factorial design under permutations of the factor levels. We code the s levels of a factor with the s-th roots of the unity. We focus on the notion of regular fraction in the complex coding, called \({{\mathbb {C}}}\)-regularity. We introduce methods to check whether a given symmetric orthogonal array can or cannot be transformed into a regular fraction by means of suitable permutations of the factor levels. The proposed techniques take advantage of the complex coding of the factor levels and of some tools from polynomial algebra. Several examples are described, mainly involving factors with five levels.

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Acknowledgements

We thank Anna Bigatti (Università di Genova) for her valuable help in using CoCoA. This work is partially funded by INdAM (National Institute for Higher Mathematics) through a GNAMPA-INdAM Project 2017. This research has a financial support of the Università del Piemonte Orientale.

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Authors and Affiliations

  1. Department of Sciences and Technological Innovation, Università del Piemonte Orientale, Alessandria, Italy

    Fabio Rapallo

  2. Dipartimento di Matematica, Università di Genova, Genoa, Italy

    Maria-Piera Rogantin

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  1. Fabio Rapallo
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  2. Maria-Piera Rogantin
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Correspondence to Maria-Piera Rogantin.

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Rapallo, F., Rogantin, MP. Algebraic Characterization of \({{\mathbb {C}}}\)-Regular Fractions Under Level Permutations. J Stat Theory Pract 13, 8 (2019). https://doi.org/10.1007/s42519-018-0012-9

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  • DOI: https://doi.org/10.1007/s42519-018-0012-9

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