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
In many experiments, the performance of a subject may be affected by some previous treatments applied to it apart from the current treatment. This motivates the studies of the residual effects of the treatments in a b...In many experiments, the performance of a subject may be affected by some previous treatments applied to it apart from the current treatment. This motivates the studies of the residual effects of the treatments in a block design. This paper shows that a circular block design neighbor-balanced at distances up toγ≤k - 1, where k is the block size, is universally optimal for total effects under the linear models containing the neighbor effects at distances up toγamong the class of all circular binary block designs. Some combinatorial approaches to constructing these circular block designs neighbor-balanced at distances up to k - 1 are provided.展开更多
In this paper, we consider the set partitioning problem with matroid constraint, which is a generation of the k-partitioning problem. The objective is to minimize the weight of the heaviest subset. We present an appro...In this paper, we consider the set partitioning problem with matroid constraint, which is a generation of the k-partitioning problem. The objective is to minimize the weight of the heaviest subset. We present an approximation algorithm, which consists of two sub-algorithms-the modified Edmonds' matroid partitioning algorithm and the exchange algorithm, for the problem. An estimation of the worst ratio for the algorithm is given.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.
基金This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10671007,10471127)Zhejiang Provincial Natural Science Foundation of China (Grant No. R604001)the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China and a CERG grant from Research Grants Council of Hong Kong
文摘In many experiments, the performance of a subject may be affected by some previous treatments applied to it apart from the current treatment. This motivates the studies of the residual effects of the treatments in a block design. This paper shows that a circular block design neighbor-balanced at distances up toγ≤k - 1, where k is the block size, is universally optimal for total effects under the linear models containing the neighbor effects at distances up toγamong the class of all circular binary block designs. Some combinatorial approaches to constructing these circular block designs neighbor-balanced at distances up to k - 1 are provided.
基金Project (No. 10671177) supported by the National Natural Science Foundation of China
文摘In this paper, we consider the set partitioning problem with matroid constraint, which is a generation of the k-partitioning problem. The objective is to minimize the weight of the heaviest subset. We present an approximation algorithm, which consists of two sub-algorithms-the modified Edmonds' matroid partitioning algorithm and the exchange algorithm, for the problem. An estimation of the worst ratio for the algorithm is given.
