An operator on ascent sequences

作者：Changtian Ying, Jiong Yu · 发表于：Wuhan University Journal of Natural Sciences · 年份：2014 · DOI：10.1007/s11859-014-1015-3 · 被引用次数：1 · 研究领域：graph theory and CDMA systems、Advanced Combinatorial Mathematics、Advanced Topics in Algebra

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.