Hankel Matrices for the Period-Doubling Sequence

نویسندگان

  • Robbert J. Fokkink
  • Cor Kraaikamp
  • Jeffrey Shallit
چکیده

We give an explicit evaluation, in terms of products of Jacobsthal numbers, of the Hankel determinants of order a power of two for the period-doubling sequence. We also explicitly give the eigenvalues and eigenvectors of the corresponding Hankel matrices.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On t-extensions of the Hankel determinants of certain automatic sequences

Abstract. In 1998, Allouche, Peyrière, Wen and Wen considered the Thue–Morse sequence, and proved that all the Hankel determinants of the period-doubling sequence are odd integers. We speak of t-extension when the entries along the diagonal in the Hankel determinant are all multiplied by t. We prove that the t-extension of each Hankel determinant of the period-doubling sequence is a polynomial ...

متن کامل

Singular Values of k-Fibonacci and k-Lucas Hankel Matrices

An exact formula was recently obtained for the spectral norms of the Lucas and Fibonacci Hankel matrices [1], and also for the Lucas and Fibonacci Toeplitz matrices [4]. These results put finishing touches on the works initiated in [2] and [3]. On another front, bounds were found for the spectral norms of k-Fibonacci and k-Lucas Toeplitz matrices [7]. In this paper, we present the exact value f...

متن کامل

A determinant characterization of moment sequences with finitely many mass-points

To a sequence (sn)n≥0 of real numbers we associate the sequence of Hankel matrices Hn = (si+j), 0 ≤ i, j ≤ n. We prove that if the corresponding sequence of Hankel determinants Dn = detHn satisfy Dn > 0 for n < n0 while Dn = 0 for n ≥ n0, then all Hankel matrices are positive semi-definite, and in particular (sn) is the sequence of moments of a discrete measure concentrated in n0 points on the ...

متن کامل

Some Aspects of Hankel Matrices in Coding Theory and Combinatorics

Hankel matrices consisting of Catalan numbers have been analyzed by various authors. DesainteCatherine and Viennot found their determinant to be ∏ 1≤i≤j≤k i+j+2n i+j and related them to the Bender Knuth conjecture. The similar determinant formula ∏ 1≤i≤j≤k i+j−1+2n i+j−1 can be shown to hold for Hankel matrices whose entries are successive middle binomial coefficients (2m+1 m ) . Generalizing t...

متن کامل

ar X iv : m at h / 05 11 12 7 v 1 [ m at h . FA ] 5 N ov 2 00 5 Factorization theory for Wiener - Hopf plus Hankel operators with almost periodic symbols

A factorization theory is proposed for Wiener-Hopf plus Hankel operators with almost periodic Fourier symbols. We introduce a factorization concept for the almost periodic Fourier symbols such that the properties of the factors will allow corresponding operator factorizations. Conditions for left, right, or both-sided invertibility of the Wiener-Hopf plus Hankel operators are therefore obtained...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • CoRR

دوره abs/1511.06569  شماره 

صفحات  -

تاریخ انتشار 2015