## Multicolored Simon Newcomb problems.(English)Zbl 0736.05007

This paper deals with generating functions for a kind of combinatorial problems known as Simon Newcomb problems. The problems can best be described in terms of shuffling a deck of cards (with certain specifications) and thereafter dividing the deck into piles according to certain rules. The problem is to determine the number of shuffles resulting in $$k+1$$ piles. The method used to count these objects consists of mapping the carddeck to a kind of “multicoloured” matrices and then counting these matrices.

### MSC:

 05A15 Exact enumeration problems, generating functions

### Keywords:

Simon Newcomb problems
Full Text:

### References:

 [1] Andrews, G. E., The theory of compositions II: Simon Newcomb’s problem, Utilitus Math., 7, 33-54 (1975) · Zbl 0326.05010 [2] Andrews, G. E., The Theory of Partitions (1976), Addision-Wesley: Addision-Wesley Reading, MA · Zbl 0371.10001 [3] Carlitz, L.; Roselle, D. P.; Scoville, R. A., Permutations and sequences with repetitions by number of increases, J. Combin. Theory, 1, 350-374 (1966) · Zbl 0304.05002 [4] Carliz, L., Enumeration of sequences by rises and falls: A refinement of the Simon Newcomb problem, Duke Math. J., 39, 267-280 (1972) · Zbl 0243.05008 [5] Désarménien, J.; Foata, D., Fonctions symétriques et séries hypergeometriques basiques multivariées, Bull. Soc. Math. France, 113, 3-22 (1985) · Zbl 0644.05005 [7] Dillon, J. F.; Roselle, D., Simon Newcomb’s problem, SIAM J. Appl. Math., 17, 1086-1093 (1969) · Zbl 0212.34701 [8] Garsia, A. M.; Gessel, I., Permutation statistics and partitions, Adv. in Math., 31, 288-305 (1979) · Zbl 0431.05007 [9] Gessel, I., Generating Functions and Enumeration of Sequences, MIT doctoral thesis (1977) [10] Goulden, I. P.; Jackson, D. M., Combinatorial Enumeration (1983), Wiley: Wiley New York · Zbl 0519.05001 [11] MacMahon, P. A., Combinatory Analysis (1915), Cambridge Univ. Press: Cambridge Univ. Press London/New York, (reprinted by Chelsea, New York, 1960) · JFM 45.1271.01 [12] Rawlings, D. P., Generalized Worpitzky identities with applications to permutation enumeration, European J. Combin, 2, 67-78 (1981) · Zbl 0471.05006 [13] Rawlings, D. P., The (q, r)-Simon Newcomb problem, J. Linear Multilinear Algebra, 10 (1981) · Zbl 0516.05004 [14] Riordan, J., An Introduction to Combinatorial Analysis (1959), Wiley: Wiley New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.