On Foulkesʹ conjecture Original Research Article

Foulkesʹ (1950) Conjecture is that if a ≤ b then id↑SawrSbSab is a subrepresentation of id↑SbwrSaSab. This paper gives three conjectures which would imply Foulkesʹ conjecture. All three conjectures are of the form of showing that a certain linear map between two combinatorial defined vector spaces is one-to-one. One of these conjectures is equivalent to a conjecture of Black and List [1]. The other two are new. Some partial results are provided.