We show that the submonoid of all n×n triangular tropical matrices satisfies a nontrivial semigroup identity and provide a generic construction for classes of such identities. The utilization of the Fibonacci number formula gives us an upper bound on the length of these 2-variable semigroup identities.
Bibliographical noteThe author thanks Glenn Merlet for the useful conversation in CIRM, Luminy, September 2011. The author would like to thank the referee for many valuable comments and helpful suggestions.
- Tropical (max-plus) matrix algebra
- Idempotent semirings
- Semigroup identities
- Semigroup varieties
- Monoid representations