Determinants and alternating sign matrices

@article{Robbins1986DeterminantsAA,
  title={Determinants and alternating sign matrices},
  author={David P. Robbins and Howard Rumsey},
  journal={Advances in Mathematics},
  year={1986},
  volume={62},
  pages={169-184}
}
Let M be an n by n matrix. By a connected minor of M of size k we mean a minor formed from k consecutive rows and k consecutive columns. We give formulas for det M in terms of connected minors, one involving minors of two consecutive sizes and one involving minors of three consecutive sizes. The formulas express det M as sums indexed by sets of alternating sign matrices. These matrices are described here and by W. H. Mills, D. P. Robbins, and H. Rumsey, Jr. (Invent. Math.66 (1982), 73–87; J… Expand
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