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dc.contributor.authorYu-Lun Changen_US
dc.identifier.citation[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).zh_TW
dc.description.abstract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。zh_TW
dc.description.abstractLet P be a normalized matching rank-unimodal poset. We can partition P into chains 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 C with length of Ci less than or equal to the length of Cj will imply the set of ranks of 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.en_US
dc.description.tableofcontentsList of Figures iv List of Tables iv 1. Introduction 1 2. Known results 5 3. Graded posets of width 14 and 15 8 4. Main theorems 11 5. Conclusion 18 References 19zh_TW
dc.subjectnested chain decompositionen_US
dc.subjectnormalized matchingen_US
dc.titleOn the Conjecture of the Nested Chain Decomposition of the Normalized Matching Posetsen_US
dc.typethesis and dissertationen_US
item.openairetypethesis and dissertation-
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