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math.CO2026
Algebraic Structures on Sets of Partitions
Madeline L. Dawsey, Megan du Preez, Rachel Van Surksum
Motivated by Robert Schneider's trailblazing work toward developing a unifying algebraic theory of integer partitions, we explore various binary operations on partitions to identif…
math.NT2026
Non-standard Zeckendorf decompositions; or, Tribonacci within Fibonacci
Katie Anders, Madeline L. Dawsey, Joseph Vandehey
We study , the number of ways of writing as a sum or difference of the first Fibonacci numbers. We show that satisfies the Tribonacci-like recurrence $B(0;…