Abstract In 1996, Edelman and Reiner defined the two higher Stasheff–Tamari orders on
triangulations of cyclic polytopes and conjectured them to coincide. We open up an …

A quotient of a poset P is a partial order obtained on the equivalence classes of an
equivalence relation  on P;  is then called a congruence if it satisfies certain conditions …

We define a poset called the Outer Tamari poset, and show it is isomorphic to a subposet of
the Tamari lattice introduced by Pallo (1986), and studied further and called the Comb poset …

The main result of this thesis is that the two higher Stasheff-Tamari orders are equal, as was
originally conjectured by Edelman and Reiner in 1996. These are two orders on the set of …

We prove two results on triangulations of even-dimensional cyclic polytopes using the
directed graphs (digraphs) implicitly associated to them by Oppermann and Thomas. First …