M. E. Mays and J. Wojciechowski, "A determinant property of Catalan numbers", Discrete Math. 211, 2000, 125 -- 133. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Some Aspects of Hankel Matrices in Coding Theory and Combinatorics - Tamm (2001) (2 citations) (Correct)
....q (k 1) n e (k 1) n e (k) n ; q (k) 1 = c k 1 c k for all k: 1:22) II. Hankel Matrices and Chebyshev Polynomials Let us illustrate the methods introduced by computing determinants of Hankel matrices whose entries are successive Catalan numbers. In several recent papers (e.g. 2] [47], 54] 62] these determinants have been studied under various aspects and formulae were given for special parameters. Desainte Catherine and Viennot in [24] provided the general solution d (k) n = Q 1 i j k 1 i j 2n i j for all n and k. This was derived as a companion formula (yielding a ....
....induction on n k. It is well known, e.g. 69] that for the Hankel matrices A (k) n with Catalan numbers as entries it is d (0) n = d (1) n = 1. For the induction beginning it must also be veri ed that d (2) n = n 1 and that d (3) n = n 1) n 2) 2n 3) 6 is the sum of squares, cf. [47], which can also be easily seen by application of recursion (2.3) Furthermore, for the matrix A (k) n whose entries are the binomial coecients 2k 1 k , 2k 3 k 1 , it was shown in [2] that d (0) n = 1 and d (1) n = 2n 1. Application of (2.3) shows that d (2) n = ....
[Article contains additional citation context not shown here]
M. E. Mays and J. Wojciechowski, \A determinant property of Catalan numbers", Discrete Math. 211, 2000, 125 - 133.
Some Aspects of Hankel Matrices in Coding Theory and Combinatorics - Tamm (2001) (2 citations) (Correct)
....= q (k 1) n e (k 1) n e (k) n ,q (k) 1 = c k 1 c k for all k. 1.22) II. Hankel Matrices and Chebyshev Polynomials Let us illustrate the methods introduced by computing determinants of Hankel matrices whose entries are successive Catalan numbers. In several recent papers (e.g. 2] [47], 54] 62] these determinants have been studied under various aspects and formulae were given for special parameters. Desainte Catherine and Viennot in [24] provided the general solution d (k) n = # 1#i#j#k 1 i j 2n i j for all n and k. This was derived as a companion formula (yielding a ....
....by induction on n k. It is well known, e.g. 69] that for the Hankel matrices A (k) n with Catalan numbers as entries it is d (0) n = d (1) n = 1. For the induction beginning it must also be verified that d (2) n = n 1andthatd (3) n = n 1) n 2) 2n 3) 6 is the sum of squares, cf. [47], which can also be easily seen by application of recursion (2.3) Furthermore, for the matrix A (k) n whose entries are the binomial coe#cients # 2k 1 k # , # 2k 3 k 1 # , it was shown in [2] that d (0) n =1andd (1) n =2n 1. Application of (2.3) shows that d (2) n = ....
[Article contains additional citation context not shown here]
M. E. Mays and J. Wojciechowski, "A determinant property of Catalan numbers", Discrete Math. 211, 2000, 125 -- 133.
Hankel Matrices in Coding Theory and Combinatorics - Tamm (2000) (Correct)
No context found.
M. E. Mays and J. Wojciechowski, "A determinant property of Catalan numbers", Discrete Math. 211, 2000, 125 -- 133.
Some Aspects of Hankel Matrices in Coding Theory and Combinatorics - Tamm (2001) (2 citations) (Correct)
No context found.
M. E. Mays and J. Wojciechowski, "A determinant property of Catalan numbers", Discrete Math. 211, 2000, 125 -- 133.
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