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 ∈ Intn and its ascent sequences, and how to determine the ascent se...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 ∈ Intn and its ascent sequences, and how to determine the ascent sequence of A＋B for kxk matrices A ∈ Int, and B ∈ Intm. We give the other definition of ascent se- quence 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 ques- tion, 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.展开更多
基金Supported by the National Natural Science Foundation of China(61262088,61063042)the Natural Science Foundation Project of Xinjiang Uygur Autonomous Region(2011211A011)
文摘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 ∈ Intn and its ascent sequences, and how to determine the ascent sequence of A＋B for kxk matrices A ∈ Int, and B ∈ Intm. We give the other definition of ascent se- quence 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 ques- tion, 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.
