Combinatorics of Khadaffi

 Given Libya's current political turmoil, and as a student studying Combinatorics (the study of counting), I must ask:  In how many different ways can you spell the name of Libya's ruthless leader?  Perhaps there is no formal construction for such a thing, but the Library of Congress and various press have used the following spellings for him*:

1. Qaddafi, Muammar
2. Al-Gathafi, Muammar
3. Al-Qadhafi, Muammar
4. Al Qathafi, Mu'ammar
5. Al Qathafi, Muammar
6. El Gaddafi, Moamar
7. El Kadhafi, Moammar
8. El Kazzafi, Moamer
9. El Qathafi, Mu'Ammar
10. Gadafi, Muammar
11. Gaddafi, Moamar
12. Gadhafi, Mo'ammar
13. Gathafi, Muammar
14. Ghadafi, Muammar
15. Ghaddafi, Muammar
16. Ghaddafy, Muammar
17. Gheddafi, Muammar
18. Gheddafi, Muhammar
19. Kadaffi, Momar
20. Kad'afi, Mu`amar al- 20
21. Kaddafi, Muamar
22. Kaddafi, Muammar
23. Kadhafi, Moammar
24. Kadhafi, Mouammar
25. Kazzafi, Moammar
26. Khadafy, Moammar
27. Khaddafi, Muammar
28. Moamar al-Gaddafi
29. Moamar el Gaddafi
30. Moamar El Kadhafi
31. Moamar Gaddafi
32. Moamer El Kazzafi
33. Mo'ammar el-Gadhafi
34. Moammar El Kadhafi
35. Mo'ammar Gadhafi
36. Moammar Kadhafi
37. Moammar Khadafy
38. Moammar Qudhafi
39. Mu`amar al-Kad'afi
40. Mu'amar al-Kadafi
41. Muamar Al-Kaddafi
42. Muamar Kaddafi
43. Muamer Gadafi
44. Muammar Al-Gathafi
45. Muammar al-Khaddafi
46. Mu'ammar al-Qadafi
47. Mu'ammar al-Qaddafi
48. Muammar al-Qadhafi
49. Mu'ammar al-Qadhdhafi
50. Mu`ammar al-Qadhdhāfī 50
51. Mu'ammar Al Qathafi
52. Muammar Al Qathafi
53. Muammar Gadafi
54. Muammar Gaddafi
55. Muammar Ghadafi
56. Muammar Ghaddafi
57. Muammar Ghaddafy
58. Muammar Gheddafi
59. Muammar Kaddafi
60. Muammar Khaddafi
61. Mu'ammar Qadafi
62. Muammar Qaddafi
63. Muammar Qadhafi
64. Mu'ammar Qadhdhafi
65. Muammar Quathafi
66. Mulazim Awwal Mu'ammar Muhammad Abu Minyar al-Qadhafi
67. Qadafi, Mu'ammar
68. Qadhafi, Muammar
69. Qadhdhāfī, Mu`ammar
70. Qathafi, Mu'Ammar el 70
71. Quathafi, Muammar
72. Qudhafi, Moammar
73. Moamar AI Kadafi
74. Maummar Gaddafi
75. Moamar Gadhafi
76. Moamer Gaddafi
77. Moamer Kadhafi
78. Moamma Gaddafi
79. Moammar Gaddafi
80. Moammar Gadhafi
81. Moammar Ghadafi
82. Moammar Khadaffy
83. Moammar Khaddafi
84. Moammar el Gadhafi
85. Moammer Gaddafi
86. Mouammer al Gaddafi
87. Muamar Gaddafi
88. Muammar Al Ghaddafi
89. Muammar Al Qaddafi
90. Muammar Al Qaddafi
91. Muammar El Qaddafi
92. Muammar Gadaffi
93. Muammar Gadafy
94. Muammar Gaddhafi
95. Muammar Gadhafi
96. Muammar Ghadaffi
97. Muammar Qadthafi
98. Muammar al Gaddafi
99. Muammar el Gaddafy
100. Muammar el Gaddafi
101. Muammar el Qaddafi
102. Muammer Gadaffi
103. Muammer Gaddafi
104. Mummar Gaddafi
105. Omar Al Qathafi
106. Omar Mouammer Al Gaddafi
107. Omar Muammar Al Ghaddafi
108. Omar Muammar Al Qaddafi
109. Omar Muammar Al Qathafi
110. Omar Muammar Gaddafi
111. Omar Muammar Ghaddafi
112. Omar al Ghaddafi

I suppose the issue here is that there is no generally accepted methodology to romanize Arabic names.  Further, his name contains several sounds that may not have an exact equivalence in English. 

Can you think of any other ways to spell his name?  How about R-U-T-H-L-E-S-S?!

*List from http://www.abcnews.com/

Adding and Counting by Ken Ono

Last Friday, I attended an Emory Public Lecture titled "Adding and Counting" by Ken Ono.  During this well attended lecture, Professor Ono beautifully revealed the new theory he and his colleagues have discovered:  that partition functions behave like fractals and a closed formula to count the number of partitions for any number n.  The results confirm an observation made by Ramanujan in 1919.



The partition function p(n) counts the number of ways a number n can be partitioned.  For instance, over addition, n=4 may be partition in five distinct ways:  1+1+1+1=1+1+2=1+3=2+2=4.  Thus, p(4)=5.  For a better idea of what it means to "behave like fractals", watch the video above and notice the same structure appears repeatedly upon zooming in.  A formula for p(n) has intrigued mathematicians for centuries.

Professor Ono joined the faculty of the Mathematics Department at Emory University last semester and I have had the pleasure of taking a Number Theory course with him last semester.  For more information on this new theory, please see the Emory eScienceCommons and AMS press release.  Congrats to Professor Ono and his team on this remarkable advancement of Mathematics!

Back to School

With 4-6 inches of snow and only 6 plows, icy Atlanta transformed to Hoth-lanta last week, resulting in a 5-day extended winter break for University students.  Although there was a delay in the start of the semester, there was no delay in discussing interesting topics in my Combinatorics course this week. 

A Steiner system with parameters l, m, n such that l<m<n is an n-element set S with an m-element subset of S (called blocks) such that any l-element subset of S is contained in exactly one block.  To simplify, let l=2 and m=3 to form a Steiner triple system S(2,3,n).  For what n does a Steiner triple system exist?
 

This question inspired Reverend Thomas Kirkman and he solved a special case of this problem in 1847.  His solution is widely known as the Kirkman Schoolgirl Problem.  So in the spirit of a fresh, new semester, here is the riddle for you:  15 girls walk to school each day in five groups of three.  How many days does it take for each pair of girls to walk together exactly once?  Note this is a Steiner triple system S(2,3,n) where n is the number of days.  Hint:  See picture.