Regular Sequences and the Joint Spectral Radius
نویسنده
چکیده
We classify the growth of a k-regular sequence based on information from its k-kernel. In order to provide such a classification, we introduce the notion of a growth exponent for k-regular sequences and show that this exponent is equal to the joint spectral radius of any set of a special class of matrices determined by the k-kernel.
منابع مشابه
Joint and Generalized Spectral Radius of Upper Triangular Matrices with Entries in a Unital Banach Algebra
In this paper, we discuss some properties of joint spectral {radius(jsr)} and generalized spectral radius(gsr) for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...
متن کاملCartesian decomposition of matrices and some norm inequalities
Let X be an n-square complex matrix with the Cartesian decomposition X = A + i B, where A and B are n times n Hermitian matrices. It is known that $Vert X Vert_p^2 leq 2(Vert A Vert_p^2 + Vert B Vert_p^2)$, where $p geq 2$ and $Vert . Vert_p$ is the Schatten p-norm. In this paper, this inequality and some of its improvements ...
متن کاملOn codes with local joint constraints
We study the largest number of sequences with the property that any two sequences do not contain specified pairs of patterns. We show that this number increases exponentially with the length of the sequences and that the exponent, or capacity, is the logarithm of the joint spectral radius of an appropriately defined set of matrices. We illustrate a new heuristic for computing the joint spectral...
متن کاملOn spectral radius of strongly connected digraphs
It is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. In this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.
متن کاملBounds on the Rate of Codes Which Forbid Specified Difference Sequences
Certain magnetic recording applications call for a large number of sequences whose differences do not include certain disallowed patterns. We show that the number of such sequences increases exponentially with their length and that the exponent, or capacity, is the logarithm of the joint spectral radius of an appropriately defined set of matrices. We derive new algorithms for determining the jo...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Int. J. Found. Comput. Sci.
دوره 28 شماره
صفحات -
تاریخ انتشار 2017