Generalized Pascal triangle for binomial coefficients of words
نویسندگان
چکیده
منابع مشابه
Generalized Pascal triangle for binomial coefficients of words
We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word. Similarly to the Sierpiński gasket that can be built as the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from Pascal triangle modulo 2, we de...
متن کاملCatalan Triangle Numbers and Binomial Coefficients
The binomial coefficients and Catalan triangle numbers appear as weight multiplicities of the finite-dimensional simple Lie algebras and affine Kac–Moody algebras. We prove that any binomial coefficient can be written as weighted sums along rows of the Catalan triangle. The coefficients in the sums form a triangular array, which we call the alternating Jacobsthal triangle. We study various subs...
متن کاملGeneralized Binomial Coefficients for Molecular Species
Let be a complex variable. We associate a polynomial in , denoted M N , to any two molecular species M = M (X) and N = N (X) by means of a binomial-type expansion of the form
متن کاملGeneralized Levinson–durbin Sequences and Binomial Coefficients
Abstract The Levinson–Durbin recursion is used to construct the coefficients which define the minimum mean square error predictor of a new observation for a discrete time, second-order stationary stochastic process. As the sample size varies, the coefficients determine what is called a Levinson–Durbin sequence. A generalized Levinson– Durbin sequence is also defined, and we note that binomial c...
متن کاملGeneralized Factorial Functions and Binomial Coefficients
Let S ⊆ Z. The generalized factorial function for S, denoted n!S , is introduced in accordance with theory already established by Bhargava ([4]). Along with several known theorems about these functions, a number of other issues will be explored. This Thesis is divided into 4 chapters. Chapter 1 provides the necessary definitions and offers a connection between the generalized factorial function...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2016
ISSN: 0196-8858
DOI: 10.1016/j.aam.2016.04.006