  Alternating sign triangles were introduced by Carroll and Speyer in relation
to cube recurrence, by analogy to alternating sign matrices for octahedron
recurrence. Permutation triangles are the alternating sign triangles whose
entries are either 0 or 1, by analogy with permutation matrices. In this paper,
we prove a simple characterization of permutation triangles, originally
conjectured by Glick. We will also prove some properties of alternating sign
triangles.
