TOPICS
Search

Simon Newcomb's Problem

Given a set P with |P|=p elements consisting of c_1 numbers 1, c_2 numbers 2, ..., and c_n numbers n and

c_1+c_2+...+c_n=p,

find the number of permutations with k-1 rises (Comtet 1974, p. 246).

See also

Euler Number

Explore with Wolfram|Alpha

References

Comtet, L. Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. Dordrecht, Netherlands: Reidel, 1974.Dillon, J. F. and Roselle, D. P. "Simon Newcomb's Problem." SIAM J. Appl. Math. 17, 1086-1093, 1969.Kreweras, G. "Sur une class de problèmes de dénombrement liés au treillis des partitions d'entiers." Cahiers Buro 6, 2-107, 1965.Kreweras, G. "Sur une extension du problème dit 'de Simon Newcomb.' " Comptes Rendus Acad. Sci. Paris 263, 43-45, 1966.Kreweras, G. "Traitement simultané du 'problème de Young' et du 'problème de Simon Newcomb.' " Cahiers Buro 10, 23-31, 1967.Riordan, J. An Introduction to Combinatorial Analysis. New York: Wiley, pp. 216 and 265, 1958.

Referenced on Wolfram|Alpha

Simon Newcomb's Problem

Cite this as:

Weisstein, Eric W. "Simon Newcomb's Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SimonNewcombsProblem.html

Subject classifications