Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/97323
 標題: 關於正則匹配偏序集之套鍊猜想的研究On the Conjecture of the Nested Chain Decomposition of the Normalized Matching Posets 作者: 張育綸Yu-Lun Chang 關鍵字: 偏序集;套鏈分解;正則匹配;Poset;nested chain decomposition;normalized matching 引用: [1] I. Anderson. Some problems in combinatorial number theory. Ph.D. Thesis. University of Nottingham.(1967). [2] I. Anderson. Combinatorics of Finite Sets. Dover Publications(2002). [3] R.P. Dilworth. A decomposition theorem for partially ordered sets. Annals of Mathematics Second Series. 51, 161-166(1950). [4] E. G. Escamilla, A. C. Nicolae, P. R. Salerno, S. Shahriari, J. O. Tirrell. On Nested Chain Decompositions of Normalized Matching Posets of Rank 3. Order 28, 357-373(2011). [5] J.R. Griggs. Sufficient conditions for a symmetric chain order. SIAM J. Appl. Math. 32, 807-809(1977). [6] T. Hsu, M. Logan, S. Shahriari. Methods for nesting rank 3 normalized matching rank-unimodal posets. Discrete Math. 309(3), 521-531(2009). [7] Y. Wang. Nested chain partitions of LYM posets, Discrete Math. 145(3), 493-497(2005). 摘要: 令P 是正則匹配單峰偏序集。我們可將P分割成一堆鏈C1, C2, ..., Cn,並且稱這些鏈所形成的集合C 是P 的一個鏈分解。 若在C 裡的任兩條鏈Ci,Cj 滿足當Ci的長度小 於等於Cj 的長度會有Ci的元素的秩的集合是Cj 的元素的秩的集合的子集合的話， 就稱C是套鏈分解，若P 有這樣的鏈分解，就稱P 可被套鏈分解。1975年 ，Griggs做了以下猜想，任何正則匹配單峰的偏序集都可被套鏈分解”。至今，只有在秩為二以及一些秩為三的偏序集被證實滿足該猜想，但在一般 的情況下是未解的。在這篇論文裡，我們回顧了前人的結果與方法，提出一些新的技巧來證實更多的秩為三的偏序集存在套鏈分解。Let P be a normalized matching rank-unimodal poset. We can partition P intochains C1;C2;...;Cn, and name C = fC1;C2;...;Cng a chain decomposition of P.The decomposition C is said to be nested, if any two different chains Ci,Cj in Cwith length of Ci less than or equal to the length of Cj will imply the set of ranksof elements in Ci is a subset of the set of those in Cj . If there exists such a chain decomposition in P, then P is nested.In 1975, Griggs conjectured thatEvery normalized matching rank-unimodal poset is nested.' Till now, the conjecture is proved to be true for all posets of rank 2 and some posets of rank 3, but it is still widely open in general.In this thesis, we will present some progress on the posets of rank 3. URI: http://hdl.handle.net/11455/97323 Rights: 同意授權瀏覽/列印電子全文服務，2017-08-02起公開。 Appears in Collections: 應用數學系所