## Abstract

A certain family of symmetric matrices, with entries ±1, is known to determine all the quartic relations that hold between multidimensional theta constants. Attention is drawn here to combinatorial properties of the shortest possible quartic relations, corresponding to vectors with minimal support in a certain eigenspace of such a matrix. A lower bound for the size of the support is established, exhibiting a "phase transition" at dimension four. The multiplicity-free eigenvectors with minimal support form an interesting combinatorial design, with a rich group of symmetries.

Original language | English |
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Pages (from-to) | 49-63 |

Number of pages | 15 |

Journal | Linear Algebra and Its Applications |

Volume | 257 |

Issue number | 1-3 |

DOIs | |

State | Published - May 1997 |

### Bibliographical note

Funding Information:The aim of this paper is twofold: We would like to present a few combinatorial results regarding certain identities involving theta functions, *Research supported in part by the Israel Science Foundation, administered by the Israel Academy of Sciences and Humanities, and by an Internal Research Grant from Bar-llan University. E-mail: radin@math, biu. ac. il. tPartially supported by the Edmund Landau Center for Research in Mathematical Analysis during a visit to the Hebrew University, Jerusalem. E-maih ykopelio@math, uci. edu. LINEAR ALGEBRA AND ITS APPLICATIONS 257:49-63 (1997)

### Funding

The aim of this paper is twofold: We would like to present a few combinatorial results regarding certain identities involving theta functions, *Research supported in part by the Israel Science Foundation, administered by the Israel Academy of Sciences and Humanities, and by an Internal Research Grant from Bar-llan University. E-mail: radin@math, biu. ac. il. tPartially supported by the Edmund Landau Center for Research in Mathematical Analysis during a visit to the Hebrew University, Jerusalem. E-maih ykopelio@math, uci. edu. LINEAR ALGEBRA AND ITS APPLICATIONS 257:49-63 (1997)

Funders | Funder number |
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Bar-Ilan University | |

Israel Academy of Sciences and Humanities | |

Israel Science Foundation |