Finite partially ordered set and some of its properties
This paper focuses on some main properties of the finite partially ordered sets. These properties are furnished in the form of theorems. Here we have presented three such theorems. The first theorem is called as ‘duality theorem’. This fundamental theorem was first obtained by Greene. Few years lat...
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| Format: | Article |
| Language: | English |
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Department of Physics, Mahendra Morang Adarsh Multiple Campus, Tribhuvan University
2015-12-01
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| Series: | Bibechana |
| Subjects: | |
| Online Access: | https://www.nepjol.info/index.php/BIBECHANA/article/view/13985 |
| _version_ | 1827250531603578880 |
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| author | RN Yadav SK Chakrabarti IS Jha UP Yadav |
| author_facet | RN Yadav SK Chakrabarti IS Jha UP Yadav |
| author_sort | RN Yadav |
| collection | DOAJ |
| description |
This paper focuses on some main properties of the finite partially ordered sets. These properties are furnished in the form of theorems. Here we have presented three such theorems. The first theorem is called as ‘duality theorem’. This fundamental theorem was first obtained by Greene. Few years later it was rediscovered and given an alternative proof by Fomin. The second theorem bestows the functionality property. The proof of this was also done by Greene. However, Gansner gave an alternative proof of the theorem taking advantage of a connection between poset and linear algebra. The proof of the third theorem is fully due to us. This theorem gives rise to a recursive computation of the shape. In the present paper we have discussed the first two properties through suitable illustrations only whereas a complete proof is furnished for the last one.
BIBECHANA 13 (2016) 126-130
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| first_indexed | 2024-04-24T05:48:53Z |
| format | Article |
| id | doaj.art-41a84a182db54de98c629b0462bcc340 |
| institution | Directory Open Access Journal |
| issn | 2091-0762 2382-5340 |
| language | English |
| last_indexed | 2025-03-22T00:05:01Z |
| publishDate | 2015-12-01 |
| publisher | Department of Physics, Mahendra Morang Adarsh Multiple Campus, Tribhuvan University |
| record_format | Article |
| series | Bibechana |
| spelling | doaj.art-41a84a182db54de98c629b0462bcc3402024-05-16T13:06:34ZengDepartment of Physics, Mahendra Morang Adarsh Multiple Campus, Tribhuvan UniversityBibechana2091-07622382-53402015-12-011310.3126/bibechana.v13i0.13985Finite partially ordered set and some of its propertiesRN Yadav0SK Chakrabarti1IS Jha2UP Yadav3Department of Mathematics, M. M. A. M. Campus, Tribhuvan University, BiratnagarDepartment of Physics, M. M. A. M. Campus, Tribhuvan University, BiratnagarDepartment of Physics, M. M. A. M. Campus, Tribhuvan University, BiratnagarDepartment of Mathematics, M. M. A. M. Campus, Tribhuvan University, Biratnagar This paper focuses on some main properties of the finite partially ordered sets. These properties are furnished in the form of theorems. Here we have presented three such theorems. The first theorem is called as ‘duality theorem’. This fundamental theorem was first obtained by Greene. Few years later it was rediscovered and given an alternative proof by Fomin. The second theorem bestows the functionality property. The proof of this was also done by Greene. However, Gansner gave an alternative proof of the theorem taking advantage of a connection between poset and linear algebra. The proof of the third theorem is fully due to us. This theorem gives rise to a recursive computation of the shape. In the present paper we have discussed the first two properties through suitable illustrations only whereas a complete proof is furnished for the last one. BIBECHANA 13 (2016) 126-130 https://www.nepjol.info/index.php/BIBECHANA/article/view/13985Posetferrers shapeduality theoremfunctionalityrecursive computation. |
| spellingShingle | RN Yadav SK Chakrabarti IS Jha UP Yadav Finite partially ordered set and some of its properties Bibechana Poset ferrers shape duality theorem functionality recursive computation. |
| title | Finite partially ordered set and some of its properties |
| title_full | Finite partially ordered set and some of its properties |
| title_fullStr | Finite partially ordered set and some of its properties |
| title_full_unstemmed | Finite partially ordered set and some of its properties |
| title_short | Finite partially ordered set and some of its properties |
| title_sort | finite partially ordered set and some of its properties |
| topic | Poset ferrers shape duality theorem functionality recursive computation. |
| url | https://www.nepjol.info/index.php/BIBECHANA/article/view/13985 |
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