A lot of combinatorial objects have algebra and coalgebra structures and posets are important combinatorial objects. In this paper, we construct algebra and coalgebra structures on the vector space spanned by posets. ...A lot of combinatorial objects have algebra and coalgebra structures and posets are important combinatorial objects. In this paper, we construct algebra and coalgebra structures on the vector space spanned by posets. Firstly, by associativity and the unitary property, we prove that the vector space with the conjunction product is a graded algebra. Then by the definition of free algebra, we prove that the algebra is free. Finally, by the coassociativity and the counitary property, we prove that the vector space with the unshuffle coproduct is a graded coalgebra.展开更多
Many research issues have been raised in Application Layer Multicasting(ALM),such as group management,security,integrity of data,link stress,link stretch,load balancing,fault tolerance and scalability,because of the s...Many research issues have been raised in Application Layer Multicasting(ALM),such as group management,security,integrity of data,link stress,link stretch,load balancing,fault tolerance and scalability,because of the shifting of the multicast protocol from the IP layer to the application layer.To address these issues many protocols have evolved by changing their topology structure.In this paper,the POSET protocol stack is proposed,which consists of three layers,such as communication control,POSET cube,and content distribution.The novelty of this paper is the lattice-based data distribution with POSET cube architecture.The results have been compared with the existing NICE and Narada protocols.The experimental results show that the proposed POSET protocol improves throughput between 7.14%and 40%and decreases the delay between 7.69%and 25%,compared to the existing NICE protocol.展开更多
Let X,Y be any posets,the semimodularity of cardinal power Yx with base Y and exponent X is studied. Some necessary or sufficient conditions for Yx to be semimodular are gaven,
Triangulated categories coming from cyclic posets were originally introduced by the authors in a previous paper as a generalization of the constructions of various triangulated categories with cluster structures.We gi...Triangulated categories coming from cyclic posets were originally introduced by the authors in a previous paper as a generalization of the constructions of various triangulated categories with cluster structures.We give an overview, and then analyze "triangulation clusters" which are those corresponding to topological triangulations of the 2-disk. Locally finite nontriangulation clusters give topological triangulations of the "cactus space" associated to the "cactus cyclic poset".展开更多
An excellent introduction to the topic of poset matroids is due to Barnabei, Nicoletti and Pezzoli. In this paper, we investigate the rank axioms for poset matroids; thereby we can characterize poset matroids in a “g...An excellent introduction to the topic of poset matroids is due to Barnabei, Nicoletti and Pezzoli. In this paper, we investigate the rank axioms for poset matroids; thereby we can characterize poset matroids in a “global” version and a “pseudo-global” version. Some corresponding properties of combinatorial schemes are also obtained.展开更多
The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent:(1) P is hypercontinuous;(2) the dual o...The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent:(1) P is hypercontinuous;(2) the dual of P is generalized completely continuous;(3) the normal completion of P is a hypercontinuous lattice. In addition, the relational representation and the intrinsic characterization of hypercontinuous posets are obtained.展开更多
In the present paper we investigate prinjective Ringel-Hall algebras,for prinjective modulesover incidence algebras of posets of finite prinjective type.Results we obtain are analogous to these.given by C.M.Ringel,for...In the present paper we investigate prinjective Ringel-Hall algebras,for prinjective modulesover incidence algebras of posets of finite prinjective type.Results we obtain are analogous to these.given by C.M.Ringel,for representations of Dynkin quivers.In particular we give a description ofprinjective Ringel-Hall algebras by generators and relations.展开更多
An excellent introduction to the topic of poset matroids is due to M. Barnabei, G. Nicoletti and L. Pezzoli. On the basis of their work, we have obtained the global rank axioms for poset matroids.In this paper, we stu...An excellent introduction to the topic of poset matroids is due to M. Barnabei, G. Nicoletti and L. Pezzoli. On the basis of their work, we have obtained the global rank axioms for poset matroids.In this paper, we study the special integral function f and obtain a new class of poset matroids from the old ones, and then we generalize this result according to the properties of f. Almost all of these results can be regarded as the application of global rank axioms for poset matroids. The main results in our paper have, indeed, investigated the restriction of the basis of the poset matroid, and we give them the corresponding geometric interpretation.展开更多
文摘A lot of combinatorial objects have algebra and coalgebra structures and posets are important combinatorial objects. In this paper, we construct algebra and coalgebra structures on the vector space spanned by posets. Firstly, by associativity and the unitary property, we prove that the vector space with the conjunction product is a graded algebra. Then by the definition of free algebra, we prove that the algebra is free. Finally, by the coassociativity and the counitary property, we prove that the vector space with the unshuffle coproduct is a graded coalgebra.
基金supported by the university Grants Commission,New Delhi,India
文摘Many research issues have been raised in Application Layer Multicasting(ALM),such as group management,security,integrity of data,link stress,link stretch,load balancing,fault tolerance and scalability,because of the shifting of the multicast protocol from the IP layer to the application layer.To address these issues many protocols have evolved by changing their topology structure.In this paper,the POSET protocol stack is proposed,which consists of three layers,such as communication control,POSET cube,and content distribution.The novelty of this paper is the lattice-based data distribution with POSET cube architecture.The results have been compared with the existing NICE and Narada protocols.The experimental results show that the proposed POSET protocol improves throughput between 7.14%and 40%and decreases the delay between 7.69%and 25%,compared to the existing NICE protocol.
基金Supported by the National Natural Science Foundation of China（60474022） Supported by the Henan Innovation Project for University Prominent Research Talents（2007KYCX018）
文摘Let X,Y be any posets,the semimodularity of cardinal power Yx with base Y and exponent X is studied. Some necessary or sufficient conditions for Yx to be semimodular are gaven,
文摘Triangulated categories coming from cyclic posets were originally introduced by the authors in a previous paper as a generalization of the constructions of various triangulated categories with cluster structures.We give an overview, and then analyze "triangulation clusters" which are those corresponding to topological triangulations of the 2-disk. Locally finite nontriangulation clusters give topological triangulations of the "cactus space" associated to the "cactus cyclic poset".
基金Supported by the National Natural Science Foundation of China (Granted No.103710438)Education Ministry of China (Granted No.02139)
文摘An excellent introduction to the topic of poset matroids is due to Barnabei, Nicoletti and Pezzoli. In this paper, we investigate the rank axioms for poset matroids; thereby we can characterize poset matroids in a “global” version and a “pseudo-global” version. Some corresponding properties of combinatorial schemes are also obtained.
基金supported by the National Natural Science Foundation of China(Nos.10861007,11161023)the National Excellent Doctoral Dissertation of China(No.2007B14)+1 种基金the Ganpo 555 Programme for Leading Talents of Jiangxi Province,the Natural Science Foundation of Jiangxi Province(No.20114BAB201008)the Fund of Education Department of Jiangxi Province(No.GJJ12657)
文摘The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent:(1) P is hypercontinuous;(2) the dual of P is generalized completely continuous;(3) the normal completion of P is a hypercontinuous lattice. In addition, the relational representation and the intrinsic characterization of hypercontinuous posets are obtained.
文摘In the present paper we investigate prinjective Ringel-Hall algebras,for prinjective modulesover incidence algebras of posets of finite prinjective type.Results we obtain are analogous to these.given by C.M.Ringel,for representations of Dynkin quivers.In particular we give a description ofprinjective Ringel-Hall algebras by generators and relations.
基金Supported partially by the National Natural Science Foundation of China(Grant No.10371048)
文摘An excellent introduction to the topic of poset matroids is due to M. Barnabei, G. Nicoletti and L. Pezzoli. On the basis of their work, we have obtained the global rank axioms for poset matroids.In this paper, we study the special integral function f and obtain a new class of poset matroids from the old ones, and then we generalize this result according to the properties of f. Almost all of these results can be regarded as the application of global rank axioms for poset matroids. The main results in our paper have, indeed, investigated the restriction of the basis of the poset matroid, and we give them the corresponding geometric interpretation.
