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math.CO2023
A Combinatorial Hopf Algebra on Partition Diagrams
John M. Campbell
We introduce a Combinatorial Hopf Algebra (CHA) with bases indexed by the partition diagrams indexing the bases for partition algebras. By analogy with the operation $H_α H_β = H_{…
math.CO2022★ 1 cited
Generalizations and variants of Knuth's old sum
Arjun K. Rathie, John M. Campbell
We extend the Reed Dawson identity for Knuth's old sum with a complex parameter, and we offer two separate hypergeometric series-based proofs of this generalization, and we apply t…