The maximum-rank-class and majority conjectures for idempotents in Jones monoids
Let Jn\mathcal{J}_nJn be the Jones monoid, let EnE_nEn be its set of idempotents, let rank(α)\operatorname{rank}(\alpha)rank(α) denote the rank of α∈En\alpha\in E_nα∈En, let en=∣En∣e_n=|E_n|en=∣En∣, and let dn∗d_n^*dn∗…