1. 123-avoiding doubly stochastic matrices.
- Author
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Brualdi, Richard A. and Cao, Lei
- Subjects
- *
STOCHASTIC matrices , *MATRICES (Mathematics) - Abstract
We investigate the convex polytope Ω n (123 ‾) of doubly stochastic matrices spanned by the n × n permutation matrices that avoid an increasing pattern of length 3, the 123 ‾ -permutation matrices. We determine some of its facets and other faces, including faces of small dimension, and their connection to facets and faces of the polytope Ω n of all n × n doubly stochastic matrices. The paper concludes with some relations concerning the frequencies of the positions of the 1's in n × n 123 ‾ -permutation matrices, and the vertex-edge graph of Ω n (123 ‾). [ABSTRACT FROM AUTHOR]
- Published
- 2024
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