Generating sets in orthogonal and symplectic rook monoids

Abstract

In this paper, we investigate the irreducible generating sets of orthogonal and symplectic rook monoids. We find that these irreducible generating sets are closely related to those of the unit groups of the monoids. We study and determine irreducible generating sets of order-preserving orthogonal rook monoids and order-preserving symplectic rook monoids. We then investigate nonirreducible generating sets of the singular parts of the orthogonal and symplectic rook monoids.

Keywords:

• Admissible subset
• generating set
• order-preserving
• orthogonal rook monoid
• symplectic rook monoid

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20M32
• 20M10

Acknowledgements

The authors thank Reginal Koo for useful comments on the manuscript, and thank the anonymous referee for valuable suggestions.