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.
- Tropical (max-plus) matrix algebra
- Idempotent semirings
- Semigroup identities
- Semigroup varieties
- Monoid representations