On the Longest Increasing Subsequence for Finite and Countable Alphabets

Christian houdré; Trevis J. Litherland

On the Longest Increasing Subsequence for Finite and Countable Alphabets

概率论 2007-05-23 v1

作者: Christian houdré , Trevis J. Litherland

摘要

Let $X_1, X_2, ..., X_n, ...$ be a sequence of iid random variables with values in a finite alphabet $\{1,...,m\}$ . Let $LI_n$ be the length of the longest increasing subsequence of $X_1, X_2, ..., X_n.$ We express the limiting distribution of $LI_n$ as functionals of $m$ and $(m-1)$ -dimensional Brownian motions. These expressions are then related to similar functionals appearing in queueing theory, allowing us to further establish asymptotic behaviors as $m$ grows. The finite alphabet results are then used to treat the countable (infinite) alphabet.

关键词

sturmian words and combinatorics on words integer sequences and recurrences collatz conjecture

引用

@article{arxiv.math/0612364,
  title  = {On the Longest Increasing Subsequence for Finite and Countable Alphabets},
  author = {Christian houdré and Trevis J. Litherland},
  journal= {arXiv preprint arXiv:math/0612364},
  year   = {2007}
}

On the Longest Increasing Subsequence for Finite and Countable Alphabets

摘要

关键词

引用

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