BibTex RIS Kaynak Göster

Weak isometries of Hamming spaces

Yıl 2016, Cilt: 3 Sayı: 3, 209 - 216, 09.08.2016
https://doi.org/10.13069/jacodesmath.67265

Öz

Consider any permutation of the elements of a (finite) metric space that preserves a specific distance
p. When is such a permutation automatically an isometry of the metric space? In this note we study
this problem for the Hamming spaces H(n,q) both from a linear algebraic and combinatorial point
of view. We obtain some sufficient conditions for the question to have an affirmative answer, as well
as pose some interesting open problems.

Kaynakça

  • P. Abramenko, H. Van Maldeghem, Maps between buildings that preserve a given Weyl distance, Indag. Math. 15(3) (2004) 305–319.
  • F. S. Beckman, D. A. Jr. Quarles, On isometries of Euclidean spaces, Proc. Amer. Math. Soc. 4 (1953) 810–815.
  • A. Brouwer, A. Cohen, A. Neumaier, Distance-Regular Graphs, Springer-Verlag, Berlin, Heidelberg, 1989.
  • A. E. Brouwer, M. A. Fiol, Distance-regular graphs where the distance d-graph has fewer distinct eigenvalues, Linear Algebra Appl. 480 (2015) 115–126.
  • S. De Winter, M. Korb, Weak isometries of the Boolean cube, Discrete Math. 339(2) (2016) 877–885.
  • E. Govaert, H. Van Maldeghem, Distance-preserving maps in generalized polygons. I. Maps on flags, Beitrage Algebra. Geom. 43(1) (2002) 89–110.
  • E. Govaert, H. Van Maldeghem, Distance-preserving maps in generalized polygons. II. Maps on points and/or lines, Beitrage Algebra Geom. 43(2) (2002) 303–324.
  • V. Yu. Krasin, On the weak isometries of the Boolean cube, Diskretn. Anal. Issled. Oper. Ser. 1 13(4) (2006) 26–32; translation in J. Appl. Ind. Math. 1(4) (2007) 463–467.
Yıl 2016, Cilt: 3 Sayı: 3, 209 - 216, 09.08.2016
https://doi.org/10.13069/jacodesmath.67265

Öz

Kaynakça

  • P. Abramenko, H. Van Maldeghem, Maps between buildings that preserve a given Weyl distance, Indag. Math. 15(3) (2004) 305–319.
  • F. S. Beckman, D. A. Jr. Quarles, On isometries of Euclidean spaces, Proc. Amer. Math. Soc. 4 (1953) 810–815.
  • A. Brouwer, A. Cohen, A. Neumaier, Distance-Regular Graphs, Springer-Verlag, Berlin, Heidelberg, 1989.
  • A. E. Brouwer, M. A. Fiol, Distance-regular graphs where the distance d-graph has fewer distinct eigenvalues, Linear Algebra Appl. 480 (2015) 115–126.
  • S. De Winter, M. Korb, Weak isometries of the Boolean cube, Discrete Math. 339(2) (2016) 877–885.
  • E. Govaert, H. Van Maldeghem, Distance-preserving maps in generalized polygons. I. Maps on flags, Beitrage Algebra. Geom. 43(1) (2002) 89–110.
  • E. Govaert, H. Van Maldeghem, Distance-preserving maps in generalized polygons. II. Maps on points and/or lines, Beitrage Algebra Geom. 43(2) (2002) 303–324.
  • V. Yu. Krasin, On the weak isometries of the Boolean cube, Diskretn. Anal. Issled. Oper. Ser. 1 13(4) (2006) 26–32; translation in J. Appl. Ind. Math. 1(4) (2007) 463–467.
Toplam 8 adet kaynakça vardır.

Ayrıntılar

Bölüm Makaleler
Yazarlar

Ryan Bruner Bu kişi benim

Stefaan De Winter Bu kişi benim

Yayımlanma Tarihi 9 Ağustos 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 3 Sayı: 3

Kaynak Göster

APA Bruner, R., & De Winter, S. (2016). Weak isometries of Hamming spaces. Journal of Algebra Combinatorics Discrete Structures and Applications, 3(3), 209-216. https://doi.org/10.13069/jacodesmath.67265
AMA Bruner R, De Winter S. Weak isometries of Hamming spaces. Journal of Algebra Combinatorics Discrete Structures and Applications. Ağustos 2016;3(3):209-216. doi:10.13069/jacodesmath.67265
Chicago Bruner, Ryan, ve Stefaan De Winter. “Weak Isometries of Hamming Spaces”. Journal of Algebra Combinatorics Discrete Structures and Applications 3, sy. 3 (Ağustos 2016): 209-16. https://doi.org/10.13069/jacodesmath.67265.
EndNote Bruner R, De Winter S (01 Ağustos 2016) Weak isometries of Hamming spaces. Journal of Algebra Combinatorics Discrete Structures and Applications 3 3 209–216.
IEEE R. Bruner ve S. De Winter, “Weak isometries of Hamming spaces”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 3, sy. 3, ss. 209–216, 2016, doi: 10.13069/jacodesmath.67265.
ISNAD Bruner, Ryan - De Winter, Stefaan. “Weak Isometries of Hamming Spaces”. Journal of Algebra Combinatorics Discrete Structures and Applications 3/3 (Ağustos 2016), 209-216. https://doi.org/10.13069/jacodesmath.67265.
JAMA Bruner R, De Winter S. Weak isometries of Hamming spaces. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3:209–216.
MLA Bruner, Ryan ve Stefaan De Winter. “Weak Isometries of Hamming Spaces”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 3, sy. 3, 2016, ss. 209-16, doi:10.13069/jacodesmath.67265.
Vancouver Bruner R, De Winter S. Weak isometries of Hamming spaces. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3(3):209-16.