Single Polygon Counting on Cayley Tree of Order 3
We showed that one form of generalized Catalan numbers is the solution to the problem of finding different connected component with finite vertices containing a fixed root for the semi-infinite Cayley tree of order 3. We give the formula for the full graph, Cayley tree of order 3 which is derived fr...
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| Format: | Article |
| Language: | English |
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Springer
2010
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| Online Access: | http://irep.iium.edu.my/293/ http://irep.iium.edu.my/293/1/Single_polygon_counting_on_cayley_tree_of_order_3_%281%29.pdf |
| _version_ | 1848775692133597184 |
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| author | Pah, Chin Hee |
| author_facet | Pah, Chin Hee |
| author_sort | Pah, Chin Hee |
| building | IIUM Repository |
| collection | Online Access |
| description | We showed that one form of generalized Catalan numbers is the solution to the problem of finding different connected component with finite vertices containing a fixed root for the semi-infinite Cayley tree of order 3. We give the formula for the full graph, Cayley tree of order 3 which is derived from the generalized Catalan numbers. Using ratios of Gamma functions, two upper bounds are given for problem defined on semi-infinite Cayley tree of order 3 as well as the full graph. |
| first_indexed | 2025-11-14T14:18:14Z |
| format | Article |
| id | iium-293 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:18:14Z |
| publishDate | 2010 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-2932011-07-11T08:02:01Z http://irep.iium.edu.my/293/ Single Polygon Counting on Cayley Tree of Order 3 Pah, Chin Hee QA Mathematics We showed that one form of generalized Catalan numbers is the solution to the problem of finding different connected component with finite vertices containing a fixed root for the semi-infinite Cayley tree of order 3. We give the formula for the full graph, Cayley tree of order 3 which is derived from the generalized Catalan numbers. Using ratios of Gamma functions, two upper bounds are given for problem defined on semi-infinite Cayley tree of order 3 as well as the full graph. Springer 2010 Article PeerReviewed application/pdf en http://irep.iium.edu.my/293/1/Single_polygon_counting_on_cayley_tree_of_order_3_%281%29.pdf Pah, Chin Hee (2010) Single Polygon Counting on Cayley Tree of Order 3. Journal of Statistical Physics, 140 (1). pp. 198-207. ISSN 0022-4715 http://dx.doi.org/10.1007/s10955-010-9989-5 10.1007/s10955-010-9989-5 |
| spellingShingle | QA Mathematics Pah, Chin Hee Single Polygon Counting on Cayley Tree of Order 3 |
| title | Single Polygon Counting on Cayley Tree of Order 3 |
| title_full | Single Polygon Counting on Cayley Tree of Order 3 |
| title_fullStr | Single Polygon Counting on Cayley Tree of Order 3 |
| title_full_unstemmed | Single Polygon Counting on Cayley Tree of Order 3 |
| title_short | Single Polygon Counting on Cayley Tree of Order 3 |
| title_sort | single polygon counting on cayley tree of order 3 |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/293/ http://irep.iium.edu.my/293/ http://irep.iium.edu.my/293/ http://irep.iium.edu.my/293/1/Single_polygon_counting_on_cayley_tree_of_order_3_%281%29.pdf |