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math.HO2025
A Closed Form for the Pulsar Sequence
Ryan Liu, Vadim Ponomarenko
In this paper, we study the Pulsar Sequence, an integer sequence derived from Latin-square-based Pulsar puzzles introduced by the Cracking the Cryptic YouTube channel. A Pulsar puz…
math.AC2025
On numerical semigroup elements and the - and -norms of their factorizations
Sogol Cyrusian, Alex Domat, Christopher O'Neill +3
A numerical semigroup is a cofinite, additively-closed subset of that contains 0, and a factorization of is a -tuple w…
math.AC2025
Betti elements and full atomic support in rings and monoids
Scott T. Chapman, Pedro García-Sánchez, Christopher O'Neill +1
Several papers in the recent literature have studied factorization properties of affine monoids using the monoid's Betti elements. In this paper, we extend this study to more gener…