# Sequences , Patterns and Coincidences

@inproceedings{Dasgupta2004SequencesP, title={Sequences , Patterns and Coincidences}, author={Anirban Dasgupta}, year={2004} }

This article provides a contemporary exposition at a moderately quantitative level of the distribution theory associated with sequences and patterns in iid multinomial trials, the birthday problem, and the matching problem. The section on patterns includes the classic distribution theory for waiting time for runs and more general patterns, and their means and moments. It also includes the central limit theorem and a.s. properties of the longest run, and modern applications to DNA sequence…

## One Citation

Foundations for Wash Sales

- Computer Science
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Consider an ephemeral sale-and-repurchase of a security resulting in the same position before the sale and after the repurchase. A sale-and-repurchase is a wash sale if these transactions result in a…

## References

SHOWING 1-10 OF 50 REFERENCES

Methods for studying coincidences

- Psychology
- 1991

This article illustrates basic statistical techniques for studying coincidences. These include data-gathering methods (informal anecdotes, case studies, observational studies, and experiments) and…

Natural sorting over permutation spaces

- Mathematics
- 1968

0. Introduction. In this paper we continue the study, begun in [1], of some combinatorial problems related to monotonicities that occur in certain spaces of finite sequences. These spaces are…

String Overlaps, Pattern Matching, and Nontransitive Games

- Mathematics, Computer ScienceJ. Comb. Theory, Ser. A
- 1981

Probability theory and combinatorial optimization

- Mathematics
- 1987

Preface 1. First View of Problems and Methods. A first example. Long common subsequences Subadditivity and expected values Azuma's inequality and a first application A second example. The…

Problems and Snapshots from the World of Probability

- Computer Science
- 1993

This book comprises a collection of 125 problems and snapshots from discrete probability that provide quick overviews of topics in probability such as Markov chains, Poisson processes, random walks, patterns in random sequences, cover times, and embedding procedures.

Poisson Approximation and the Chen-Stein Method

- Mathematics
- 1990

The Chen-Stein method of Poisson approximation is a powerful tool for computing an error bound when approximating probabilities using the Poisson distribution. In many cases, this bound may be given…

Concentration of measure and isoperimetric inequalities in product spaces

- Mathematics
- 1994

The concentration of measure phenomenon in product spaces roughly states that, if a set A in a product ΩN of probability spaces has measure at least one half, “most” of the points of Ωn are “close”…

Sequence Comparison Significance and Poisson Approximation

- Computer Science
- 1994

Poisson approximation techniques using the Aldous clumping heuristic to a practical method of estimating statistical significance of sequence alignment scores with gaps are extended.

LIMIT DISTRIBUTIONS OF MAXIMAL SEGMENTAL SCORE AMONG MARKOV-DEPENDENT PARTIAL SUMS

- Mathematics
- 1992

Let s1, " , sn be generated governed by an r-state irreducible aperiodic Markov chain. The partial sum process S.,m = 1E' Xss,si+,, m = 1, 2, - - - is determined by a realization {s})=o of states…

On the distribution of the length of the longest increasing subsequence of random permutations

- Mathematics
- 1998

Let SN be the group of permutations of 1,2,..., N. If 7r E SN, we say that 7(i1),... , 7F(ik) is an increasing subsequence in 7r if il < i2 < ... < ik and 7r(ii) < 7r(i2) < ...< 7r(ik). Let 1N(r) be…