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math.CO2024
Even and odd compositions with restricted parts
Jia Huang
A result of Legendre asserts that the difference between the numbers of (length) even and odd partitions of into distinct parts is , , or ; this also follows from Eul…
math.CO2024
Associative-commutative spectra for some varieties of groupoids
Jia Huang, Erkko Lehtonen
The associative spectrum of a groupoid (i.e., a set with a binary operation) measures its nonassociativity while the associative-commutative spectrum measures both nonassociativity…