Geodesic
Sequences by Number of w-Rises
Canadian mathematical bulletin, Tome 18 (1975) no. 3, pp. 317-319

Voir la notice de l'article provenant de la source Cambridge University Press

An m-permutation of n, repetitions allowed, is an m-sequence (1) A w-rise is a pair (ei, ei+1) such that ei+1-ei≥w>0. In this note we find an expression for Tk, w(n, m), the number of m-sequences having precisely k w-rises. The case w = 1 is given in [1] [2]. Also, when w = 1 we give the number when each of the integers 1, 2, ..., r must appear at least once. 
Abramson, Morton. Sequences by Number of w-Rises. Canadian mathematical bulletin, Tome 18 (1975) no. 3, pp. 317-319. doi: 10.4153/CMB-1975-059-6
@article{10_4153_CMB_1975_059_6,
     author = {Abramson, Morton},
     title = {Sequences by {Number} of {w-Rises}},
     journal = {Canadian mathematical bulletin},
     pages = {317--319},
     year = {1975},
     volume = {18},
     number = {3},
     doi = {10.4153/CMB-1975-059-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-059-6/}
}
TY  - JOUR
AU  - Abramson, Morton
TI  - Sequences by Number of w-Rises
JO  - Canadian mathematical bulletin
PY  - 1975
SP  - 317
EP  - 319
VL  - 18
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-059-6/
DO  - 10.4153/CMB-1975-059-6
ID  - 10_4153_CMB_1975_059_6
ER  - 
%0 Journal Article
%A Abramson, Morton
%T Sequences by Number of w-Rises
%J Canadian mathematical bulletin
%D 1975
%P 317-319
%V 18
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-059-6/
%R 10.4153/CMB-1975-059-6
%F 10_4153_CMB_1975_059_6

[1] 1. Carlitz, L., Roselle, D. P. and Scoville, R. A., Permutations and sequences with repetitions by number of increases, J. Comb. Theory 1 (1966), pp. 350-374. Google Scholar

[2] 2. Dillon, J. F. and Roselle, D. P., Simon Newcomb's problem, SIAM J. Appl. Math. 17 (1969), pp. 1086-1093. Google Scholar

[3] 3. Gould, H. W., Combinatorial Identities, West Virginia University, Morgantown, West Virginia, 1972. Google Scholar

[4] 4. Moser, W. O. J. and Morton, Abramson, Enumeration of Combinations with restricted differences andcospan, J. Comb. Theory 7 (1969), pp. 162-170. Google Scholar

[5] 5. Riordan, J., An introduction to combinatorial analysis, J. Wiley, New York, 1958. Google Scholar

Cité par Sources :