Record Compositions of Alternating Permutations
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Statement
Amdeberhan, Shareshian and Stanley showed a function from the theory of partition Eisenstein series counts alternating permutations with a given record partition, and asked whether a similar theory exists for record compositions, suggesting a role for noncommutative symmetric functions. The paper solves that open problem with a product formula.
Context
Solves a problem posed by Stanley and coauthors in the theory of partition Eisenstein series, and does so with a machine-checked proof.
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