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2013 | 1 | 17-24
Tytuł artykułu

A note on majorization transforms and Ryser’s algorithm

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The notion of a transfer (or T -transform) is central in the theory of majorization. For instance, it lies behind the characterization of majorization in terms of doubly stochastic matrices. We introduce a new type of majorization transfer called L-transforms and prove some of its properties. Moreover, we discuss how L-transforms give a new perspective on Ryser’s algorithm for constructing (0; 1)-matrices with given row and column sums.
Wydawca
Czasopismo
Rocznik
Tom
1
Strony
17-24
Opis fizyczny
Daty
otrzymano
2013-09-12
zaakceptowano
2013-09-30
online
2013-10-29
Twórcy
autor
  • Department of Mathematics, University of Oslo,
    P.O. Box 1053 Blindern, NO-0316 Oslo, Norway, geird@math.uio.no
Bibliografia
  • [1] R. Bhatia, Matrix Analysis, Springer, New York, 1997.
  • [2] R.A. Brualdi, Combinatorial Matrix Classes, Cambridge University Press, Cambridge, 2006.
  • [3] R.A. Brualdi, Matrices of zeros and ones with fixed row and column sum vectors, Linear Algebra Appl. 33 (1980),159-231.
  • [4] R.A. Brualdi, P. Gibson, Convex polyhedra of doubly stochastic matrices, II. Graph of Ωn, J. Combin. Theory Ser. A22 (1977), 175-198.
  • [5] R.A. Brualdi, P. Gibson, Convex polyhedra of doubly stochastic matrices, III. Affine and combinatorial properties of Ωn, J. Combin. Theory Ser. A 22 (1977), 338-351.
  • [6] L. Costa, C.M. da Fonseca, E.A. Martins, The diameter of the acyclic Birkhoff polytope, Linear Algebra Appl. 428(2008), 1524-1537.[WoS]
  • [7] G. Dahl, Tridiagonal doubly stochastic matrices, Linear Algebra Appl. 390 (2004), 197-208.
  • [8] G. Dahl, F. Zhang, Integral majorization polytopes, Discrete Math. Algorithm. Appl. DOI: 10.1142/S1793830913500195.[Crossref]
  • [9] C.M. da Fonseca, E.M. de Sá, Fibonacci numbers, alternating parity sequences and faces of the tridiagonal Birkhoffpolytope, Discrete Math. 308 (2008), 1308-1318.[WoS]
  • [10] G.H. Hardy, J.E. Littlewood, G. Pólya, Inequalities, (First ed. 1934, 2nd ed. 1952), Cambridge University Press,Cambridge Mathematical Library, 2, 1988.
  • [11] J.H. van Lint, R.M. Wilson, A Course in Combinatorics, Cambridge University Press, Cambridge, 2001.
  • [12] A.W. Marshall, I. Olkin, B.C. Arnold, Inequalities: Theory of Majorization and Its Applications, Second edition,Springer, New York, 2011.[WoS]
  • [13] R.F. Muirhead, Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters,Proc. Edinb. Math. Soc. 21 (1902), 144-157.
  • [14] E.M. de Sá, Some subpolytopes of the Birkhoff polytope, Electron. J. Linear Algebra 15 (2006), 1-7.
  • [15] F. Zhang, Matrix Theory - Basic Results and Techniques, Springer, New York, 2011.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_spma-2013-0004
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