Pattern-avoidance characterization of lci K-orbit closures

Let $G=GL(p+q,\mathbb{C})$, $K=GL(p,\mathbb{C})\times GL(q,\mathbb{C})$, and consider $K$-orbit closures in $G/B$, indexed by clans. A clan avoids a pattern when it contains no occurrence of that pattern, with negatives of patterns included when specified. Pattern-avoidance conjecture for lci K-orbit closures. LCI-ness of $K$-orbit closures for $(GL(p+q,\mathbb{C}),GL(p,\mathbb{C})\times GL(q,\mathbb{C}))$ is characterized by pattern avoidance. In other words, a $K$-orbit closure is lci if and only if its indexing clan avoids the patterns that characterize lci-ness. Computations verify the characterization through $p+q\leq 8$, but the authors do not claim that the displayed finite list of additional bad patterns is complete; the conjecture remains open because checks at $p+q=9$ were unavailable.