## Abstract

We propose a perturbation method for determining the (largest) group of invariance of a toric ideal defined in [S. Aoki, A. Takemura, The largest group of invariance for Markov bases and toric ideals, J. Symbolic Comput. 43 (5) (2008) 342-358]. In the perturbation method, we investigate how a generic element in the row space of the configuration defining a toric ideal is mapped by a permutation of the indeterminates. Compared to the proof by Aoki and Takemura which was based on stabilizers of a subset of indeterminates, the perturbation method gives a much simpler proof of the group of invariance. In particular, we determine the group of invariance for a general hierarchical model of contingency tables in statistics, under the assumption that the numbers of the levels of the factors are generic. We prove that it is a wreath product indexed by a poset related to the intersection poset of the maximal interaction effects of the model.

Original language | English |
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Pages (from-to) | 375-389 |

Number of pages | 15 |

Journal | Advances in Applied Mathematics |

Volume | 43 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2009 Oct |

Externally published | Yes |

## Keywords

- Computational algebraic statistics
- Group action
- Stabilizer
- Sudoku
- Wreath product

## ASJC Scopus subject areas

- Applied Mathematics