2 problems

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Maximum-upset conjecture for the permutation $\rho(t)$
Maximum-upset conjecture. The permutation $\rho(t)$ is a rank- $t$ permutation with the maximum number of rank- $r$ permutations in its upset.
Conjectureopenextremal-combinatorics permutation-statistics weak-bruhat-latticearXiv posted 2 days ago
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EKR conjecture for levels of the weak Bruhat lattice
Weak Bruhat lattice EKR conjecture. For all values of $1\le r\le \frac12{n\choose2}$ , the set ${\mathscr B}_n(r)$ is EKR. Thus, for any $p\in{\mathscr B}_n(1)$ ,
Conjectureopenerdos-ko-rado permutation-intersecting-families weak-bruhat-latticearXiv posted 2 days ago

Maximum-upset conjecture for the permutation ρ(t)\rho(t)ρ(t)