3.R: References
- Page ID
- 3133
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- N. L. Biggs, “The Roots of Combinatorics," Historia Mathematica, vol. 6 (1979), pp. 109–136.
- P. R. de Montmort, Essay d’Analyse sur des Jeux de Hazard, 2d ed. (Paris: Quillau, 1713).
- F. N. David, Games, Gods and Gambling (London: Griffin, 1962), p. 146.
- M. vos Savant, Ask Marilyn, , 21 August 1994.
- J. Riordan, (New York: John Wiley & Sons, 1958).
- P. Doyle, “Solution to Montmort’s Probleme du Treize,” math.ucsd.edu/\(\tilde{\ }\)doyle/.
- P. Doyle, C. Grinstead, and J. Snell, “Frustration Solitaire," , vol. 16, no. 2 (1995), pp. 137-145.
- R. von Mises, “Über Aufteilungs- und Besetzungs-Wahrscheinlichkeiten," Revue de la Faculté des Sciences de l’Université d’Istanbul, N. S. vol. 4 (1938-39), pp. 145-163.
- W. Feller, vol. 1, 3rd ed. (New York: John Wiley & Sons, 1968).
- J. Stirling, Methodus Differentialis, (London: Bowyer, 1730).
- A. de Moivre, The Doctrine of Chances, 3rd ed. (London: Millar, 1756).
- H. S. Wilf, “A Bijection in the Theory of Derangements," vol. 57, no. 1 (1984), pp. 37–40.
- E. B. Dynkin and A. A. Yushkevich, trans. J. S. Wood (New York: Plenum, 1969).
- W. Feller, vol. 1, 3rd ed. (New York: John Wiley and Sons, 1968), p. 41
- B. Pascal, (Paris: Desprez, 1665).
- A. W. F. Edwards, (London: Griffin, 1987).
- ibid., p. 27.
- J. Needham, vol. 3 (New York: Cambridge University Press, 1959), p. 135.
- N. Tartaglia, (Vinegia, 1556).
- Quoted in Edwards, op. cit., p. 37.
- M. Stifel, (Norimburgae, 1544).
- G. Cardano, (Basilea, 1570).
- F. N. David, op. cit., p. 235.
- A. W. F. Edwards, op. cit., p. ix.
- J. Bernoulli, (Basil: Thurnisiorum, 1713).
- W. Feller, vol. I, 3rd ed. (New York: John Wiley & Sons, 1968), p. 106.
- E. Lucas, “Théorie des Functions Numériques Simplement Periodiques," vol. 1 (1878), pp. 184-240, 289-321.
- B. Mann, “How Many Times Should You Shuffle a Deck of Cards?", , vol. 15, no. 4 (1994), pp. 303–331.
- D. Bayer and P. Diaconis, “Trailing the Dovetail Shuffle to its Lair," , vol. 2, no. 2 (1992), pp. 294–313.