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math.CO2018
Compositions with restricted parts
Jia Huang
Euler showed that the number of partitions of into distinct parts equals the number of partitions of into odd parts. This theorem was generalized by Glaisher and further by…
math.CO2018
Variations of the Catalan numbers from some nonassociative binary operations
Nickolas Hein, Jia Huang
We investigate certain nonassociative binary operations that satisfy a four-parameter generalization of the associative law. From this we obtain variations of the ubiquitous Catala…