Eulerian triangle is totally positive of order 3

Abstract

Brenti conjectured that the Eulerian triangle is totally positive. In this paper, we prove that the Eulerian triangle is totally positive of order 3, thereby providing a partial affirmative answer to Brenti's conjecture. In addition, we establish total positivity of order 3 for several families of generalized Eulerian triangles.

arXiv comment18 pages, 0 figure