Faces of faces of the tridiagonal Birkhoff polytope

The tridiagonal Birkhoff polytope, , is the set of real square matrices with nonnegative entries and all rows and columns sums equal to 1 that are tridiagonal. This polytope arises in many problems of enumerative combinatorics, statistics, combinatorial optimization, etc. In this paper, for a given a p-face of , we determine the number of faces of lower dimension that are contained in it and we discuss its nature. In fact, a 2-face of is a triangle or a quadrilateral and the cells can only be tetrahedrons, pentahedrons or hexahedrons.