The gold partition conjecture and the Lexicographic sum of posets

Eric R. Dolores-Cuenca, Aldo Guzmán-Sáenz, Sangil Kim

We prove that if a finite poset $Q$ satisfies the Gold Partition Conjecture, and $P$ is a finite poset, then for any $i\in P$ the lexicographic sum $P{\circ }_{i}Q$ of $P$ with $Q$ on t…