Open Positivity Conjectures for Integer Partitions

  title={Open Positivity Conjectures for Integer Partitions},
  author={Dan Stanton},
The purpose of this report is to collect some open positivity conjectures for integer partitions. The conjectures in §2-§3 are simple to state and initially appear easy to do, but remain open. The conjectures in §4-§5 should be related to representation theory, since they generalize known facts in this area. The conjectures in §6 are speculative, and if true, would require new combinatorial insight. We will use standard notation found in [1] throughout. The q-shifted factorials are defined by