### Abstract

We prove that the sum of entries of the suitably normalized groundstate vector of the O(1) loop model with periodic boundary conditions on a periodic strip of size 2n is equal to the total number of n × n alternating sign matrices. This is done by identifying the state sum of a multi-parameter inhomogeneous version of the O(1) model with the partition function of the inhomogeneous six-vertex model on a n × n square grid with domain wall boundary conditions.

Original language | English (US) |
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Article number | R6 |

Pages (from-to) | 1-27 |

Number of pages | 27 |

Journal | Electronic Journal of Combinatorics |

Volume | 12 |

Issue number | 1 R |

State | Published - Jan 11 2005 |

Externally published | Yes |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics

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## Cite this

Di Francesco, P., & Zinn-Justin, P. (2005). Around the Razumov-Stroganov conjecture: Proof of a multi-parameter sum rule.

*Electronic Journal of Combinatorics*,*12*(1 R), 1-27. [R6].