Partitions with prescribed hooksets
William J. Keith (University of Lisbon), Rishi Nath (CUNY-York)
TL;DR
This paper investigates the combinatorial properties of partitions with specific hookset restrictions, linking them to numerical semigroups and extending results on simultaneous s/t-cores.
Contribution
It introduces new conditions for partitions to have prescribed hooks and explores their connection with numerical semigroups.
Findings
Extended current results on simultaneous s/t-cores.
Developed conditions for partitions to possess required hooks.
Explored the combinatorial properties of hookset-restricted partitions.
Abstract
The combinatorial properties of partitions with various restrictions on their hooksets are explored. A connection with numerical semigroups extends current results on simultaneous s/t-cores. Conditions that suffice for a partition to possess required hooks are developed.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · semigroups and automata theory