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,
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
In this paper, some properties of order topology and bi-Scott topology on a poset are obtained. Order-convergence in posets is further studied. Especially, a sufficient and necessary condition for order-convergence to...In this paper, some properties of order topology and bi-Scott topology on a poset are obtained. Order-convergence in posets is further studied. Especially, a sufficient and necessary condition for order-convergence to be topological is given for some kind of posers.展开更多
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 M.Barnabei, G. Nicoletti and L. Pezzoli. On the basis of their work, we have obtained the global rankaxioms for poset matroids. In this paper, we stud...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 rankaxioms for poset matroids. In this paper, we study the special integral function f and obtain a newclass of poset matroids from the old ones, and then we generalize this result according to theproperties of f. Almost all of these results can be regarded as the application of global rankaxioms for poset matroids. The main results in our paper have, indeed, investigated the restrictionof the basis of the poset matroid, and we give them the corresponding geometric interpretation.展开更多
In the present paper we investigate prinjective Ringel-Hall algebras, for prinjective modules over incidence algebras of posers of finite prinjective type. Results we obtain are analogous to these, given by C. M. Ring...In the present paper we investigate prinjective Ringel-Hall algebras, for prinjective modules over incidence algebras of posers 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 of prinjective Ringel-Hall algebras by generators and relations.展开更多
Taking domains in the one hand and actions of a semigroup （automaton） on the other, as two crucial notions in mathematics as well as in computer science, we consider the notion of compact directed complete poset （a...Taking domains in the one hand and actions of a semigroup （automaton） on the other, as two crucial notions in mathematics as well as in computer science, we consider the notion of compact directed complete poset （acts）, and investigate the interesting notion of absolute retractness for such ordered structures. As monomorphisms and embeddings for domain acts are different notions, we study absolute retractness with respect to both the class of monomorphisms and that of embed- dings for compact directed complete poset （acts）. We characterize the absolutely retract compact dcpos as complete compact chains. Also, we give some examples of compact di- rected complete poset acts which are （g-）absolutely retract （with respect to embeddings） and show that completeness is not a sufficient condition for （g-）absolute retractness.展开更多
Let F denote the folded （2D ＋ 1）-cube with vertex set X and diameter D ≥ 3. Fix x∈ X. We first define a partial order ≤ on X as follows. For y,z ∈ X let y ≤ z whenever （x,y）＋ （y,z） =- （x, z）. Let R ...Let F denote the folded （2D ＋ 1）-cube with vertex set X and diameter D ≥ 3. Fix x∈ X. We first define a partial order ≤ on X as follows. For y,z ∈ X let y ≤ z whenever （x,y）＋ （y,z） =- （x, z）. Let R （resp. L） denote the raising matrix （resp. lowering matrix） of P. Next we show that there exists a certain linear dependency among RL2, LRL, L2R and L for each given Q-polynomial structure of F. Finally, we determine whether the above linear dependency structure gives this poser a uniform structure or strongly uniform structure.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,
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 National Natural Science Foundation of China （Grant Nos. 10871121, 11001158）
文摘In this paper, some properties of order topology and bi-Scott topology on a poset are obtained. Order-convergence in posets is further studied. Especially, a sufficient and necessary condition for order-convergence to be topological is given for some kind of posers.
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 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 rankaxioms for poset matroids. In this paper, we study the special integral function f and obtain a newclass of poset matroids from the old ones, and then we generalize this result according to theproperties of f. Almost all of these results can be regarded as the application of global rankaxioms for poset matroids. The main results in our paper have, indeed, investigated the restrictionof the basis of the poset matroid, and we give them the corresponding geometric interpretation.
文摘In the present paper we investigate prinjective Ringel-Hall algebras, for prinjective modules over incidence algebras of posers 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 of prinjective Ringel-Hall algebras by generators and relations.
文摘Taking domains in the one hand and actions of a semigroup （automaton） on the other, as two crucial notions in mathematics as well as in computer science, we consider the notion of compact directed complete poset （acts）, and investigate the interesting notion of absolute retractness for such ordered structures. As monomorphisms and embeddings for domain acts are different notions, we study absolute retractness with respect to both the class of monomorphisms and that of embed- dings for compact directed complete poset （acts）. We characterize the absolutely retract compact dcpos as complete compact chains. Also, we give some examples of compact di- rected complete poset acts which are （g-）absolutely retract （with respect to embeddings） and show that completeness is not a sufficient condition for （g-）absolute retractness.
基金Supported by the Natural Science Foundation of China(No.11471097)the Innovative Fund Project of Hebei Province(sj.2017084)
文摘Let F denote the folded （2D ＋ 1）-cube with vertex set X and diameter D ≥ 3. Fix x∈ X. We first define a partial order ≤ on X as follows. For y,z ∈ X let y ≤ z whenever （x,y）＋ （y,z） =- （x, z）. Let R （resp. L） denote the raising matrix （resp. lowering matrix） of P. Next we show that there exists a certain linear dependency among RL2, LRL, L2R and L for each given Q-polynomial structure of F. Finally, we determine whether the above linear dependency structure gives this poser a uniform structure or strongly uniform structure.
