Contents
Research Article
Young tableaux and longest monotone subsequences: An inequality and a conjecture
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- 20 January 2009, pp. 341-344
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Much work has been done on the following problem, which is sometimes referred to as Ulam's problem: what is the distribution of
, the length (i.e. number of terms) of a longest monotone increasing [decreasing] subsequence of (not necessarily consecutive) terms in a random permutation of the first N integers? For example, it has been shown that 
converges almost surely to 2 [6,7,9]. In some cases, it is important to know the value of βN(j), the number of permutations for which αN=j
, the length (i.e. number of terms) of a longest monotone increasing [decreasing] subsequence of (not necessarily consecutive) terms in a random permutation of the first 
converges almost surely to 2 [Book Reviews
G. James and A. Kerber, The representation theory of the symmetric group (Encyclopedia of Mathematics and its Applications, Vol. 16, Addison-Wesley, Reading, Mass., 1981), pp. 510, £37.80.
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- 20 January 2009, pp. 103-104
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J. Aczél (ed.), Functional equations: history, applications and theory (D. Reidel, Dordrecht1984), pp. ix + 244, Dfl. 125.
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- 20 January 2009, pp. 345-346
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Front matter
PEM volume 27 issue 1 Cover and Front matter
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- 20 January 2009, pp. f1-f2
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Book Reviews
J. M. Ball,(ed) Systems of nonlinear partial differential equations (D. Reidel, Dordrecht, 1983), ix + 481 pp., Dfl. 150.
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- 20 January 2009, pp. 235-236
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Back matter
PEM volume 27 issue 1 Cover and Back matter
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- 20 January 2009, p. b1
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Book Reviews
B. A. Barnes, G. J. Murphy, M. R. F. Smyth and T. T. West, Riesz and Fredholm theory in Banach algebras (Research Notes in Mathematics 67, Pitman, 1982), 123 pp, £7.95.
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- 20 January 2009, p. 346
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Front matter
PEM volume 27 issue 2 Cover and Front matter
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- Published online by Cambridge University Press:
- 20 January 2009, pp. f1-f2
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Back matter
PEM volume 27 issue 2 Cover and Back matter
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- Published online by Cambridge University Press:
- 20 January 2009, p. b1
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Book Reviews
K. T. Smith, Primer of modern analysis (Springer-Verlag, 2nd ed.1983), xv + 446 pp. DM97.
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- 20 January 2009, pp. 346-347
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Wilhelm Blaschke, Gesammelte Werke, Band I ed. by W. Burau, S. S. Chern et al. (Thales-Verlag, Essen1982), pp. 365.
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- 20 January 2009, pp. 347-349
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J. Diestel, Sequences and series in Banach spaces (Graduate Texts in Mathematics Vol. 92, Springer-Verlag, Berlin-Heidelberg-New York, 1984) xiii + 261 pp., DM 108.
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- 20 January 2009, p. 349
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P. A. Perry, Scattering theory by the Enss method (Mathematical Reports Vol. 1, Part 1, Harwood Academic Publishers, New York, 1983) xiv + 347 pp., $82.
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- 20 January 2009, p. 350
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Fornt matter
PEM volume 27 issue 3 Cover and Fornt matter
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- 20 January 2009, pp. f1-f2
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Back matter
PEM volume 27 issue 3 Cover and Back matter
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- 20 January 2009, pp. b1-b6
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