Recurrence Relations and Hilbert Series of the Monoid Associated with Star Topology
Affine monoids are the considered as natural discrete analogues of the finitely generated cones. The interconnection between these two objects has been an active area of research since last decade. Star network is one of the most common in computer network topologies. In this work, we study star top...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/5215631 |
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| _version_ | 1832550348639698944 |
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| author | Jiang-Hua Tang Zaffar Iqbal Abdul Rauf Nizami Mobeen Munir Faiza Azam Jia-Bao Liu |
| author_facet | Jiang-Hua Tang Zaffar Iqbal Abdul Rauf Nizami Mobeen Munir Faiza Azam Jia-Bao Liu |
| author_sort | Jiang-Hua Tang |
| collection | DOAJ |
| description | Affine monoids are the considered as natural discrete analogues of the finitely generated cones. The interconnection between these two objects has been an active area of research since last decade. Star network is one of the most common in computer network topologies. In this work, we study star topology Sn and associate a Coxeter structure of affine type on it. We find a recurrence relation and the Hilbert series of the associated right-angled monoid MSn∞. We observe that the growth rate of the monoid MSn∞ is unbounded. |
| format | Article |
| id | doaj-art-4944edc827ef477a85b2125bb89f92f7 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-4944edc827ef477a85b2125bb89f92f72025-02-03T06:06:55ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/52156315215631Recurrence Relations and Hilbert Series of the Monoid Associated with Star TopologyJiang-Hua Tang0Zaffar Iqbal1Abdul Rauf Nizami2Mobeen Munir3Faiza Azam4Jia-Bao Liu5Department of General Education, Anhui Xinhua University, Hefei 230088, ChinaDepartment of Mathematics, University of Gujrat, Gujrat, PakistanUniversity of Central Punjab, Department of Mathematics, Lahore, PakistanDepartment of Mathematics, Division of Science and Technology, University of Education Township, Lahore, PakistanDepartment of Mathematics, University of Gujrat, Gujrat, PakistanSchool of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, ChinaAffine monoids are the considered as natural discrete analogues of the finitely generated cones. The interconnection between these two objects has been an active area of research since last decade. Star network is one of the most common in computer network topologies. In this work, we study star topology Sn and associate a Coxeter structure of affine type on it. We find a recurrence relation and the Hilbert series of the associated right-angled monoid MSn∞. We observe that the growth rate of the monoid MSn∞ is unbounded.http://dx.doi.org/10.1155/2020/5215631 |
| spellingShingle | Jiang-Hua Tang Zaffar Iqbal Abdul Rauf Nizami Mobeen Munir Faiza Azam Jia-Bao Liu Recurrence Relations and Hilbert Series of the Monoid Associated with Star Topology Journal of Mathematics |
| title | Recurrence Relations and Hilbert Series of the Monoid Associated with Star Topology |
| title_full | Recurrence Relations and Hilbert Series of the Monoid Associated with Star Topology |
| title_fullStr | Recurrence Relations and Hilbert Series of the Monoid Associated with Star Topology |
| title_full_unstemmed | Recurrence Relations and Hilbert Series of the Monoid Associated with Star Topology |
| title_short | Recurrence Relations and Hilbert Series of the Monoid Associated with Star Topology |
| title_sort | recurrence relations and hilbert series of the monoid associated with star topology |
| url | http://dx.doi.org/10.1155/2020/5215631 |
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