By Jørn Børling Olsson
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Additional info for Combinatorics and Representations of Finite Groups
R. P. Stanley, Enumerative Combinatorics, Vol. 1, Wadsworth (1986). J. Stedall, Symbolism, combinations, and visual imagery in the mathematics of Thomas Harriot, Historia Math. 34 (2007), 380–401, on p. 398. T. Strode, Short Treatise of the Combinations, Elections, Permutations and Composition of Quantities, London (1678), 19–20. F. Swetz, Leibniz, the Yijing, and the religious conversion of the Chinese, Math. Mag. 76 (2003), 276–91. A. Tacquet, Arithmeticæ Theoria et Praxis, Louvain (1656). N.
Cayley’s major work on trees , originally published in 1875, was climaxed by a large foldout illustration that exhibited all of the free (unrooted) trees with nine or fewer unlabelled vertices. Earlier in that paper he had also illustrated the nine oriented (rooted) trees with five vertices. The methods he used to produce those lists were quite complicated. All free trees with up to ten vertices were listed many years later by F. Harary and G. Prins , who also went up to n = 12 in the cases of free trees with no vertices of degree 2 or with no symmetries.
54. J. Prestet, Nouveaux Elémens des Mathématiques, Paris (1689), 127–33. 55. E. Puteanus, Pietatis Thaumata, Antwerp (1617). 56. J. Scaliger, Poetices Libri Septem, Book 2, Lyon (1561), Ch. 30, p. 73. 36 | c o m b i n ato r i c s : a n c i e n t a n d m o d e r n 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. J. Schillinger, The Schillinger System of Musical Composition, Carl Fischer (1946). F. van Schooten, Exercitationes Mathematicæ, Johannes Elzevier, Leiden (1657). H. I.