Problems / combinatorics

combinatorics / Enumerative Combinatorics, Symmetric Functions

Record Compositions of Alternating Permutations

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.