کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
436126 689974 2015 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On t-extensions of the Hankel determinants of certain automatic sequences
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
On t-extensions of the Hankel determinants of certain automatic sequences
چکیده انگلیسی

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 in t, whose leading coefficient is the only one to be an odd integer. Our proof makes use of the combinatorial set-up developed by Bugeaud and Han, which appears to be very suitable for this study, as the parameter t counts the number of fixed points of a permutation. Finally, we prove that all the t-extensions of the Hankel determinants of the regular paperfolding sequence are polynomials in t of degree less than or equal to 3.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Theoretical Computer Science - Volume 562, 11 January 2015, Pages 46–56
نویسندگان
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