Lower bounds on the size of spheres of permutations under the Chebychev distance

Designs, Codes, and Cryptography

Volumn 59, Issue 1-3, 2011, Pages 183-191

  Kløve, Torleiv ^a  

^a UNIVERSITY OF BERGEN   (Norway)

Author keywords

Chebychev distance; Permutations; Spheres

Indexed keywords

CHEBYCHEV DISTANCE; LOWER BOUNDS; PERMUTATIONS;

SPHERES;

EID: 79953276899     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10623-010-9454-0     Document Type: Conference Paper

References (13)

1. Baltić V.: On the number of certain types of restricted permutations. In: Abstracts of Talks presented at the International Mathematical Conference, Topics in Mathematical Analysis and Graph Theory (MAGT). Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. 18, 93-137 (2007).
2. H.W. Gould 1965 An identity involving Stirling numbers Ann. Inst. Stat. Math. 17 265 269 10.1007/BF02868171
3. Jiang A., Mateescu R., Schwartz M., Bruck J.: Rank modulation for flash memories. In: Proceedings of IEEE International Symposium on Information Theory, pp. 1731-1735 (2008).
4. Jiang A., Schwartz M., Bruck J.: Error-correcting codes for rank modulation. In: Proceedings of IEEE International Symposium on Information Theory, pp. 1736-1740 (2008).
5. Kløve T.: Spheres of permutations under the infinity norm-permutations with limited displacement. Report no. 2008-376, Department of Informatics, University of Bergen, Norway. http://www.ii.uib.no/publikasjoner/ texrap/pdf/2008-376.pdf.
6. T. Kløve T.-T. Lin S.-C. Tsai W.-G. Tzeng 2010 Permutation arrays under the Chebyshev distance IEEE Trans. Inform. Theory 56 6 2611 2617 2683423 10.1109/TIT.2010.2046212
7. R. Lagrange 1962 Quelques résultats dans la métrique des permutations Annales Scientifiques de l'École Normale Supérieure 79 199 241 151402
8. Lehmer D.H.: Permutations with strongly restricted displacements. In: Erdös P., Rńyi A., Sós V.T. (eds.) Combinatorial Theory and its Applications II. North Holland Publication, Amsterdam, pp. 755-770 (1970).
9. Peterson W.W., Weldon E.J.: Error-Correcting Codes. MIT Press, Cambridge (1972)
10. Sloane N.J.A.: The On-Line Encyclopedia of Integer Sequences. http://www.research.att.com/~njas/sequences/.
11. Stanley R.P.: Enumerative Combinatorics, vol. I. Cambridge University Press, Cambridge (1997)
12. I. Tamo M. Schwartz 2010 Correcting Limited-Magnitude Errors in the Rank-Modulation Scheme IEEE Trans. Inform. Theory 56 6 2551 2560 2683416 10.1109/TIT.2010.2046241
13. van Lint J.H., Wilson R.M.: A Course in Combinatorics, 2nd edn. Cambridge University Press, Cambridge (2001)