Hankel determinants for convolution powers of Catalan numbers

Wang, Ying; Xin, Guoce

doi:10.1016/j.disc.2019.05.025

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Cited by 5 publications

(2 citation statements)

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“…By using the transformation τ we have discovered some shifted periodic continued fractions for H n (C(x) r ) with r ≤ 9, and seems the computation for much larger r is possible. These will appear in an upcoming paper [21].…”

Section: Concluding Remarkmentioning

confidence: 88%

Hankel determinants and shifted periodic continued fractions

Wang

Xin

Zhai³

2019

Advances in Applied Mathematics

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Sulanke and Xin developed a continued fraction method that applies to evaluate Hankel determinants corresponding to quadratic generating functions. We use their method to give short proofs of Cigler's Hankel determinant conjectures, which were proved recently by Chang-Hu-Zhang using direct determinant computation. We find that shifted periodic continued fractions arise in our computation. We also discover and prove some new nice Hankel determinants relating to lattice paths with step set {(1, 1), (q, 0), ( −1, −1)} for integer parameters m, q, . Again shifted periodic continued fractions appear.Mathematic subject classification: Primary 15A15; Secondary 05A15, 11B83.

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Section: Concluding Remarkmentioning

confidence: 88%

Hankel determinants and shifted periodic continued fractions

Wang

Xin

Zhai³

2019

Advances in Applied Mathematics

Self Cite

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“…The Hankel transform of the sequence {a 0 , a 1 , a 2 , ...} is the Hankel determinant of the form det(a i+j+r ) n−1 i,j=0 , where r is a non-negative integer (see [3]). For r = 0, 1, 2, and let (a n ) n≥0 be the Catalan squence (C n ) n≥0 , there are many results [1][2] [5][6] [8]. But there is no result for n > 5.…”

Section: Introductionmentioning

confidence: 99%