We settle a question of Bressoud concerning the existence of an explicit bijection from a class of oriented square-ice graphs to a class of tournaments by giving an algorithmic construction of such a bijection.
Pattern Avoidance in Alternating Sign Matrices
β Scribed by Robert Johansson; Svante Linusson
- Publisher
- Springer
- Year
- 2007
- Tongue
- English
- Weight
- 171 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0218-0006
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π SIMILAR VOLUMES
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 for
The sign pattern matrix A is called sign k-potent if k is the smallest positive integer such that e k1 eX The structure of irreducible, sign k-potent pattern matrices was characterized by Stuart et al. (J. Stuart, C. Eschenbach, S. Kirkland, Linear Algebra Appl. 294 (1999) 85Β±92). We extend those re
The sign pattern matrix A is called sign k-potent if k is the smallest positive integer for which e k1 eX We characterize the irreducible pattern matrices that are sign k-potent and provide a canonical form for such matrices.