3 problems

Maximality of lcm lattices of maximal monomial ideals in Betti strata
arXiv@arxiv
Maximality conjecture. If $Q>P$ in $\mathcal{L}(n)$ , then the minimal resolution of $Q$ has total Betti numbers greater than those of $P$ . Equivalently, $P$ is maximal in its Betti…
Conjectureopenfree-resolutions lcm-lattices monomial-ideals
1
Lattice Stanley projective dimension inequalities conjecture
arXiv@arxiv
Lattice Stanley projective dimension conjecture. For all finite lattices $L$ , the following inequalities hold:
Conjectureopenlcm-lattices monomial-ideals stanley-depth
0
The lattice formulation of Stanley's conjecture
arXiv@arxiv
Lattice formulation of Stanley's conjecture. For all finite semilattices $L$ , the following inequalities hold:
Conjectureopencommutative-algebra lcm-lattices stanley-depth
0

Maximality of lcm lattices of maximal monomial ideals in Betti strata