Part-products of S-restricted Integer Compositions
نویسندگان
چکیده
If S is a cofinite set of positive integers, an “S-restricted composition of n” is a sequence of elements of S, denoted ~λ = (λ1, λ2, . . . ), whose sum is n. For uniform random S-restricted compositions, the random variable B(~λ) = ∏ i λi is asymptotically lognormal. (A precise statement of the theorem includes an error term to bound the rate of convergence.) The proof is based upon a combinatorial technique for decomposing a composition into a sequence of smaller compositions.
منابع مشابه
Restricted Weighted Integer Compositions and Extended Binomial Coefficients
We prove a simple relationship between extended binomial coefficients — natural extensions of the well-known binomial coefficients — and weighted restricted integer compositions. Moreover, we give a very useful interpretation of extended binomial coefficients as representing distributions of sums of independent discrete random variables. We apply our results, e.g., to determine the distribution...
متن کاملParallel Algorithm for Second-Order Restricted Weak Integer Composition Generation for Shared Memory Machines
In 2012, Page presented a sequential combinatorial generation algorithm for generalized types of restricted weak integer compositions called second–order restricted weak integer compositions. Second–order restricted weak integer compositions cover various types of restricted weak integer compositions of n parts such as integer compositions, bounded compositions, and part–wise integer compositio...
متن کاملMaximum Part-Products of Odd Palindromic Compositions
We derive explicit formulas for the maximum part-product over the set of palindromic compositions of a given integer and over the set of palindromic compositions of a given integer with only odd parts. These results are extensions of the well-known elementary formula for the maximum part-product over the set of classical partitions.
متن کاملCorrections to the results derived in "A Unified Approach to Algorithms Generating Unrestricted and Restricted Integer Compositions and Integer Partitions"'; and a comparison of four restricted integer composition generation algorithms
In this note, I discuss results on integer compositions/partitions given in the paper “A Unified Approach to Algorithms Generating Unrestricted and Restricted Integer Compositions and Integer Partitions”. I also experiment with four different generation algorithms for restricted integer compositions and find the algorithm designed in the named paper to be pretty slow, comparatively. Some of my ...
متن کاملPart-Products of 1-Free Integer Compositions
If ~λ is a composition of the positive integer n, define B(~λ) to be the product of the parts of ~λ. We present a modified version of Hitczenko’s stopped sequence construction that leads to a proof of the asymptotic lognormality of B for random 1-free compositions (compositions containing no parts of size 1).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011