Determinants and alternating sign matrices

✍ Scribed by David P Robbins; Howard Rumsey Jr.

• Publisher: Elsevier Science
• Year: 1986
• Tongue: English
• Weight: 666 KB
• Volume: 62
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1016/0001-8708(86)90099-x

✦ Synopsis

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 A4 as sums indexed by sets of alternating sign matrices. These matrices are described here and by W. H.