An operator on ascent sequences

We solve two problems about ascent sequences: how to get the ascent sequence of the reflection of A with respect to its antidiagonal for a matrix A ∈ Int _n and its ascent sequences, and how to determine the ascent sequence of A+B for k×k matrices A ∈ Int _n and B ∈ Int _m . We give the other definition of ascent sequence and get M-sequence. For the first question, we define M-sequence of A and rewrite the ascent sequences as another form. We build the bijection between M-sequences and ascent sequences and prove that our bijection is well-defined. For the second question, we define an operation on M-sequences. On the basis of the operation and the bijections, we get the ascent sequences of the sum of two matrices.