Avoiding patterns and making the best choice

@article{Jones2019AvoidingPA,
  title={Avoiding patterns and making the best choice},
  author={Brant C. Jones},
  journal={Discret. Math.},
  year={2019},
  volume={342},
  pages={1529-1545}
}
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References

SHOWING 1-10 OF 26 REFERENCES
Recognizing the Maximum of a Sequence
Abstract The classical dowry, secretary, or beauty contest problem is extended in several directions. In trying to find sequentially the maximum of a random sequence of fixed length, the chooser can
Secretary Problems with Non-Uniform Arrival Order
TLDR
This work initiates an investigation into relaxations of the random-ordering hypothesis in online algorithms, by focusing on the secretary problem and asking what performance guarantees one can prove under relaxed assumptions, and proves that Θ(log log n) is the minimum entropy of any permutation distribution that permits constant probability of correct selection in the secretaries problem with $n$ elements.
Online auctions and generalized secretary problems
TLDR
This work presents generalized secretary problems as a framework for online auctions, and presents surprisingly strong constant factor guarantees on the expected value of solutions obtained by online algorithms.
Who Solved the Secretary Problem
TLDR
The object of this article is to give a fresh view of the origins of the problem, touching upon Cayley and Kepler, and review of the field (listing the subfields of recent interest), partly serious (to answer the question posed in the title), and partly entertainment.
A GENERALIZATION OF THE CLASSICAL SECRETARY PROBLEM: DEPENDENT ARRIVAL SEQUENCES
This paper presents new methods for selecting the best population value under the classical secretary problem sequential selection rules. Unlike the classical case, the possible population arrival
Structure of random 312‐avoiding permutations
TLDR
The exact formulas for the probability that the ith element of a random permutation is a specific value less than i are derived, and for joint probabilities of two such events are obtained.
Longest Increasing Subsequences in Pattern-Restricted Permutations
TLDR
The limiting distributions for pattern-restricted permutations in which the pattern is any one of the six patterns of length 3 are found, and it is shown that the (132)-avoiding case is identical to the distribution of heights of ordered trees, and the (321) case has interesting connections with a well known theorem of Erd\H os-Szekeres.
What is known about Robbins' Problem?
Let X 1 , X 2 , ..., X n be independent, identically distributed random variables, uniform on [0,1]. We observe the X k sequentially and must stop on exactly one of them. No recollection of the
The shape of random pattern-avoiding permutations
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