This paper presents a bijection between ascent sequences and upper triangular
matrices whose non-negative entries are such that all rows and columns contain
at least one non-zero entry. We show the equivalence of several natural
statistics on these structures under this bijection and prove that some of
these statistics are equidistributed. Several special classes of matrices are
shown to have simple formulations in terms of ascent sequences. Binary matrices
are shown to correspond to ascent sequences with no two adjacent entries the
same. Bidiagonal matrices are shown to be related to order-consecutive set
partitions and a simple condition on the ascent sequences generate this class.Comment: 13 page