810
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

On One Type of Generalized Vandermonde Determinants

REFERENCES

  • Alexandersson, P. (2012). Schur polynomials, banded Toeplitz matrices and Widom’s formula. Electron. J. Combin. 19(4): Paper #P22, 1--13.
  • Bareiss, E. H. (1968). Sylvester’s identity and multistep integer-preserving Gaussian elimination. Math. Comp. 22(103): 565–578.
  • Basor, E. (1978). Asymptotic formulas for Toeplitz determinants. Trans. Amer. Math. Soc. 239: 33–65.
  • Baxter, G., Schmidt, P. (1961). Determinants of a certain class of non-Hermitian Toeplitz matrices. Math. Scand. 9: 122–128.
  • Cinkir, Z. (2010). Volumes of n-simplices with vertices on a polynomial space curve. AIP Conf. Proc. 1309(213): 213–218.
  • Elouafi, M. (2014). On a relationship between Chebyshev polynomials and Toeplitz determinants. Appl. Math. Comput. 229: 27–33.
  • Flowe, R. P., Harris, G. A. (1993). A note on generalized Vandermonde determinants. SIAM J. Matrix Anal. Appl. 14(4): 1146–1151.
  • Heineman, E. R. (1929). Generalized Vandermonde determinants. Trans. Amer. Math. Soc. 31(3): 464–476.
  • King, R. C. (1975). Generalized Vandermonde determinants and Schur functions. Proc. Amer. Math. Soc. 48(1): 53–56.
  • Krasovsky, I. (2011). Aspects of Toeplitz determinants. In: Lenz, D., Sobieczky, F., Woess, W., eds. Random Walks, Boundaries and Spectra. Progress in Probability, Vol. 64. Basel: Springer, pp. 305–324. link.springer.com/chapter/10.1007/978-3-0346-0244-0_16
  • Kuipers, L., Meulenbeld, B. (1955). Symmetric polynomials with non negative coefficients. Proc. Amer. Math. Soc. 6(1): 88–93.
  • Macdonald, I. G. (1995). Symmetric Functions and Hall Polynomials, 2nd ed. Oxford: Oxford University Press.
  • Neuman, E. (1988). On complete symmetric functions. SIAM J. Math. Anal. 19(3): 736–750.
  • Press, W. H., Teukolsky, S. A., Vetterling, W. T., Flannery, B. P. (1992). Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd ed. Cambridge: Cambridge University Press.
  • Rahman, Q. I., Schmeisser, G. (2002). Analytic Theory of Polynomials. Oxford: Clarendon Press, Oxford University Press.
  • Rosenbloom, P. C. (1946). Some properties of absolutely monotonic functions. Bull. Amer. Math. Soc. 52(6): 458–462.
  • Sobczyk, G. (2002). Generalized Vandermonde determinants and applications. Aportaciones Mat. 30: 41–53.
  • Stanley, R. P. (1999). Enumerative Combinatorics, Vol. 2. Cambridge: Cambridge University Press.
  • Trench, W. F. (1985). On the eigenvalue problem for Toeplitz band matrices. Linear Algebra Appl. 64: 199–214.
  • Widom, H. (1973). Toeplitz determinants with singular generating functions. Amer. J. Math. 95(2): 333–383.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.