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EVALUATING SOME DETERMINANTS OF MATRICES WITH RECURSIVE ENTRIES

  • Moghaddamfar, Ali Reza (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE K. N. TOOSI UNIVERSITY OF TECHNOLOGY) ;
  • Salehy, Seyyed Navid (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE K. N. TOOSI UNIVERSITY OF TECHNOLOGY) ;
  • Salehy, Seyyed Nima (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE K. N. TOOSI UNIVERSITY OF TECHNOLOGY)
  • Published : 2009.03.31

Abstract

Let ${\alpha}$ = (${\alpha}_1,\;{\alpha}_2$,...) and ${\beta}$ = (${\beta}_1,\;{\beta}_2$,...) be two sequences with ${\alpha}_1$ = ${\beta}_1$ and k and n be natural numbers. We denote by $A^{(k,{\pm})}_{{\alpha},{\beta}}(n)$ the matrix of order n with coefficients ${\alpha}_{i,j}$ by setting ${\alpha}_{1,i}$ = ${\alpha}_i,\;{\alpha}_{i,1}$ = ${\beta}_i$ for 1 ${\leq}$ i ${\leq}$ n and $${\alpha}_{i,j}=\{{\alpha}_{i-1,j-1}+{\alpha}_{i-1,j}\;if\;j{\equiv}$$2,3,4,..., k + 1 (mod 2k) $$\{{\alpha}_{i-1,j-1}-{\alpha}_{i-1,j}\;if\;j{\equiv}$$ k + 2,..., 2k + 1 (mod 2k) for 2 ${\leq}$ i, j ${\leq}$ n. The aim of this paper is to study the determinants of such matrices related to certain sequence ${\alpha}$ and ${\beta}$ and some natural numbers k.

Keywords

References

  1. R. Bacher, Determinants of matrices related to the Pascal triangle, J. Theor. Nombres Bordeaux 14 (2002), no. 1, 19–41
  2. C. Krattenthaler, Advanced determinant calculus, Sem. Lothar. Combin. 42 (1999), Art. B42q, 67 pp
  3. C. Krattenthaler, Evaluations of some determinants of matrices related to the Pascal triangle, Sem. Lothar. Combin. 47 (2001/02), Art. B47g, 19 pp

Cited by

  1. The determinants of matrices constructed by subdiagonal, main diagonal and superdiagonal vol.31, pp.3, 2010, https://doi.org/10.1134/S1995080210030133