Geodesic
An Induction Theorem for Rearrangements
Canadian journal of mathematics, Tome 28 (1976) no. 1, pp. 154-160

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

In this paper, an induction theorem for rearrangements involving w-tuples in Rn is proved, showing that a certain proposition regarding a pair of w-tuples related by the weak spectral order ≪ is true for any integer n ≧ 2 if and only if it is true for n = 2. This theorem contains as particular cases a well-known theorem of Hardy-Littlewood-Pólya [4, Lemma 2, p. 47], a theorem of Pólya [8], a theorem of Rado [9, pp. 1-2], two theorems of Mirsky [6, Theorem 2, p. 232; 7, Theorem 4, p. 90], a result given in [1, Corollary 2.4, p. 1333] and also [2, Proposition 2.1, p. 439]. 
Chong, Kong-Ming. An Induction Theorem for Rearrangements. Canadian journal of mathematics, Tome 28 (1976) no. 1, pp. 154-160. doi: 10.4153/CJM-1976-019-4
@article{10_4153_CJM_1976_019_4,
     author = {Chong, Kong-Ming},
     title = {An {Induction} {Theorem} for {Rearrangements}},
     journal = {Canadian journal of mathematics},
     pages = {154--160},
     year = {1976},
     volume = {28},
     number = {1},
     doi = {10.4153/CJM-1976-019-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-019-4/}
}
TY  - JOUR
AU  - Chong, Kong-Ming
TI  - An Induction Theorem for Rearrangements
JO  - Canadian journal of mathematics
PY  - 1976
SP  - 154
EP  - 160
VL  - 28
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-019-4/
DO  - 10.4153/CJM-1976-019-4
ID  - 10_4153_CJM_1976_019_4
ER  - 
%0 Journal Article
%A Chong, Kong-Ming
%T An Induction Theorem for Rearrangements
%J Canadian journal of mathematics
%D 1976
%P 154-160
%V 28
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-019-4/
%R 10.4153/CJM-1976-019-4
%F 10_4153_CJM_1976_019_4

[1] 1. Chong, K. M., Some extensions of a theorem of Hardy, Littlew∞d and Pôlya and their applications, Can. J. Math. 26 (1974), 1321–1340. Google Scholar

[2] 2. Chong, K. M., Spectral order preserving matrices and Muirhead's theorem, Trans. Amer. Math. Soc. 200 (1974), 437–444. Google Scholar

[3] 3. Chong, K. M., A general induction theorem for rearrangements of n-tuples, J. Math. Anal. Appl. (to appear). Google Scholar

[4] 4. Hardy, G. H., Littlew∞d, J. E. and G., Pôlya, Inequalities (Cambridge, 1959). Google Scholar

[5] 5. Marshall, A. W. and Proschan, F., An inequality for convex functions involving majorization, J. Math. Anal. Appl. 12 (1965), 87–90. Google Scholar

[6] 6. Mirsky, L., Inequalities for certain classes of convex functions, Proc. Edin. Math. Soc. 11 (1959), 231–235. Google Scholar

[7] 7. Mirsky, L., On a convex set of matrices, Archiv der Math. 10 (1959), 88–92. Google Scholar

[8] 8. Pôlya, G., Remark on WeyVs note: Inequalities between the two kinds of eigenvalues of a linear transformation, Proc. Nat. Acad. Sci., 36 (1950), 49–51. Google Scholar

[9] 9. Rado, R., An inequality, J. London Math. Soc. 27 (1952), 1–6. Google Scholar

Cité par Sources :