In the context of Lie (super)algebras of type A, generalized quantum statistics is considered. For sl(n + 1) this is A-statistics, and for sl(1|n) this is A-superstatistics. The creation and annihilation operators, their triple relations, and their Fock spaces are given. We consider a 'free' Hamiltonian and some macroscopic properties are studied: the grand partition function, average number of particles, etc. Symmetric functions play a role in expressions for these thermodynamical quantities.
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