臺灣博碩士論文加值系統

在這篇論文中，我們繼續陳國傑博士應用Abel's identity在整數分割上的證明方式。我們主要推導出新的整數分割方式，其中是有關於Andrews and Stanley的identities，以及Yee's identities。並且用Abel's identity給予新的証明方式。

In this paper, we continue the work of Kuo-Jye Chen on applications of an identity of Abel to integer partitions.
Our work leads to a new identity related to partition functions of Andrews and Stanley.

審定簽名頁 I
論文授權書 II
中文摘要 III
英文摘要 IV
致謝辭 V
目錄 VI
表目錄 VII
1 Introduction 1
2 A derivation of a three-parameter generating function of Q^{(k, l)}(N, m, n) 4
3 New Derivation of Yee's Identities 6
3.1 Main theorem 6
3.2 Lemmas 8
3.3 Proof of Theorem 3.2(i) 19
3.4 Proof of Theorem 3.2(ii) 21
3.5 Proof of Theorem 3.2(iii) 23
3.6 Proof of Theorem 3.2(iv) 26
Acknowledgements 30
References 31
Appendix i
Table 1 Special cases of Equation 3.1 ii
Table 2 Special cases of Equation 3.2 iv
Table 3 Special cases of Equation 3.3 vii
Special cases of Theorem 3.2(iii)[Yee's identity] xi
Table 4 Special cases of Equation 3.4 xii

References

[1]NielsHenrikAbel,Untersuchungen¨uberdieReihe 1+(m/1)+(m(m+1)/2!)x^2+..., Journal f¨ur die reine und angewandte Mathematik, Band1(1826), 311–339.

[2]G.E.Andrews, The Theory of Partitions, Cambridge Unversity Press, 1998.

[3]G.E.Andrews, On apartition function of Richard Stanley, The Electronic Journal of Combinatorics, 11(2), 2004, #R1.

[4]G.E.Andrews, R.AskeyandR.Roy, Specialfunctions, volume71 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, 1999.

[5]K.–J.Chen, Arefinement of apartition theorem of Sellers, INTEGERS, The Electronic Journal of Combinatorial Number Theory, 4, 2004, #A15.


[6]K.–J.Chen, private communication(2004).

[7]K.–J.Chen, Sums of aweight function of Cilanne Boulet, manuscript(2005).

[8]J.A.Sellers, Extending arecent result of San to sonpartitions into oddparts, INTEGERS:Electronic Journal of Combinatorial Number Theory, 3 (2003), #A04.


[9]J.A.Sellers, Corrigendum to Article A4, 3(2003), INTEGERS 4 (2004), #A08.


[10]R.P.Stanley, Problem 10969 Amer.Math.Monthly, 109 (2002), 760.

[11]R.P.Stanley, Some remarks on sign-balanced andmajbalanced posets, to appear in Advances in Applied Math, available from http://www.math.mit.edu/~rstan/.

[12]Ae Ja Yee, On partition functions of Andrews and Stanley, Journal of Combinatorial Theory, SeriesA, 107 (2004), 313–321.