Partitions with prescribed hooksets

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.

12 pages

References in corpus (1)

• Counting numerical sets with no small atoms

Cited by in corpus (7)

• Numerical Sets, Core Partitions, and Integer Points in Polytopes
• The number of simultaneous core partitions
• Partitions with parts separated by parity: conjugation, congruences and the mock theta functions
• On the largest sizes of certain simultaneous core partitions with distinct parts
• Symmetric and Pseudo-Symmetric Numerical Semigroups via Young Diagrams and Their Semigroup Rings
• On the polynomiality and asymptotics of moments of sizes for random $(n,dn\pm 1)$-core partitions with distinct parts
• Partitions with fixed largest hook length