Geodesic
Permutations with Confined Displacements
Canadian mathematical bulletin, Tome 4 (1961) no. 1, pp. 29-38

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

A fundamental problem in combinatorial analysis is the classification of the permutations of 1, 2, ..., n which satisfy a system of constraints. Thus one may ask such questions as how many permutations are there which have exactly r k-cycles; how many have at least s cycles regardless of cycle length. Again, one may ask how many permutations are there in which k ascending sequences appear; or how many permutations are there in which specified numbers may not appear in specified places or at specified distances from other numbers. The literature on these problems is quite extensive. References [1,2,5,7,10,14,17] give an indication of the present, status of these problems. 
Mendelsohn, N. S. Permutations with Confined Displacements. Canadian mathematical bulletin, Tome 4 (1961) no. 1, pp. 29-38. doi: 10.4153/CMB-1961-005-4
@article{10_4153_CMB_1961_005_4,
     author = {Mendelsohn, N. S.},
     title = {Permutations with {Confined} {Displacements}},
     journal = {Canadian mathematical bulletin},
     pages = {29--38},
     year = {1961},
     volume = {4},
     number = {1},
     doi = {10.4153/CMB-1961-005-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1961-005-4/}
}
TY  - JOUR
AU  - Mendelsohn, N. S.
TI  - Permutations with Confined Displacements
JO  - Canadian mathematical bulletin
PY  - 1961
SP  - 29
EP  - 38
VL  - 4
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1961-005-4/
DO  - 10.4153/CMB-1961-005-4
ID  - 10_4153_CMB_1961_005_4
ER  - 
%0 Journal Article
%A Mendelsohn, N. S.
%T Permutations with Confined Displacements
%J Canadian mathematical bulletin
%D 1961
%P 29-38
%V 4
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1961-005-4/
%R 10.4153/CMB-1961-005-4
%F 10_4153_CMB_1961_005_4

[1] 1. Fréchet, M., Les probabilités associées à un système d1 événements compatible et dépendant II(Paris, 1943). Google Scholar

[2] 2. Gontcharoff, W., Sur la distribution des cycles dans les permutations, Dokl. Akad. Nauk SSSR, 35 (1942), 267-269. Google Scholar

[3] 3. Hall, Marshall, A combinatorial theorem for Abelian groups, Proc. Amer. Math. Soc. 3 (1952), 584-587. Google Scholar

[4] 4. Kaplansky, I., On a generalization of the "problème des rencontres", Amer. Math. Monthly, 46 (1939), 159-161. Google Scholar

[5] 5. Kaplansky, I., Symbolic solution of certain problems in permutations, Bull. Amer. Math. Soc. 50 (1944), 906-914. Google Scholar

[6] 6. Kaplansky, I., Solution of the "problème des ménages", Bull. Amer. Math. Soc. 49 (1943), 784-785. Google Scholar

[7] 7. Kaplansky, I., and Riordan, J., The problem of the rooks and its applications, Duke Math, J. 13 (1946), 259-268. Google Scholar

[8] 8. Kaplansky, I., and Erdös, P., The asymptotic number of latin rectangles, Amer. J. Math. 68 (1946), 230-236. Google Scholar

[9] 9. Kerewala, S. M., The enumeration of the latin rectangles of depth three by means of a difference equation, Bull. Calcutta Math. Soc. 33 (1941), 119-127. Google Scholar

[10] 10. Mendelsohn, N. S., The asymptotic series for a certain class of permutation problem, Canad. J. Math. 8 (1956), 243-244. Google Scholar

[11] 11. Mendelsohn, N. S., Symbolic solution of card matching problems, Bull. Amer. Math. Soc. 52 (1946),918-924. Google Scholar

[12] 12. Mendelsohn, N. S., Dulmage, A. L. and Johnson, D. M., Orthomorphisms of groups and orthogonal latin squares, Canad. J. Math. Google Scholar

[13] 13. Moser, L. and Wyman, M., On solutions of xd = 1 in symmetric groups, Canad. J. Math. 7 (1955), 159-168. Google Scholar

[14] 14. Riordan, J., Combinatorial Analysis, (New York, 1958), Chapters 3, 4, 7, 8. Google Scholar

[15] 15. Riordan, J., Three line latin rectangles, Amer. Math. Monthly 51 (1944), 450-452. Google Scholar

[16] 16. Riordan, J. Three line latin rectangles II, Amer. Math. Monthly 53 (1946), 18-20. Google Scholar

[17] 17. Touchard, J., Sur les cycles des substitutions, Acta. Math. 70 (1939), 243-279. Google Scholar

[18] 18. Yamamoto, K., The asymptotic series for three line rectangles, J. Math. Soc. Japan 1 (1949), 226-241. Google Scholar

Cité par Sources :