  A $(2k+1)-$dimensional Lie algebra is called contact if it admits a one-form
$\varphi$ such that $\varphi\wedge(d\varphi)^k\neq 0.$ Here, we extend recent
work to describe a combinatorial procedure for generating contact, type-A Lie
poset algebras whose associated posets have chains of arbitrary cardinality,
and we conjecture that our construction leads to a complete characterization.

Rings and Algebras;Combinatorics