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Journal article
On limiting distributions of Graham, Knuth, Patashnik recurrences
Journal of Combinatorial Theory Series A, v 277, 106270
Apr 2027
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Abstract
Graham, Knuth and Patashnik in their book Concrete Mathematics called for development of a general theory of the solutions of recurrences defined by ⃓ ⃓ ⃓ n k ⃓ ⃓ ⃓ ⃓ =(αn+βk+γ) ⃓ ⃓ ⃓ n−1 ⃓ ⃓ ⃓ +(α′n+β′k+γ′) k ⃓ ⃓ ⃓ ⃓ n−1 k−1 ⃓ ⃓ ⃓ +In=k=0 for 0 ≤ k ≤ n and six parameters α,β,γ,α′β′,γ′. Since then, a number of authors investigated various properties of the solutions of these recurrences. In this note we consider a probabilistic aspect, namely we consider the limiting distributions of sequences of integer valued random variables naturally associated with the solutions of such recurrences. We will give a complete description of the limiting behavior when α′ =0and the remaining five parameters are nonnegative.
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Details
- Title
- On limiting distributions of Graham, Knuth, Patashnik recurrences
- Creators
- Pawel Hitczenko (Corresponding Author) - Drexel University, Mathematics
- Publication Details
- Journal of Combinatorial Theory Series A, v 277, 106270
- Publisher
- Elsevier
- Number of pages
- 24
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001885686100001
- Other Identifier
- 991022209145604721