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The algebra of symmetric functions contains several interesting families of symmetric functions indexed by integer partitions or skew partitions. Given a sequence ₙ\ of symmetric functions taken from one of these families such that uₙ is homogeneous of degree n, we provide necessary and sufficient conditions for the sequence to form a system of algebraically independent generators for the algebra of symmetric functions.
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S. Velmurugan (2024) studied this question.
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