scholarly journals The Distribution of the Length of the Longest Increasing Subsequence in Random Permutations of Arbitrary Multi-sets

2019 ◽  
Vol 22 (3) ◽  
pp. 1009-1021
Author(s):  
Ayat Al-Meanazel ◽  
Brad C. Johnson
Keyword(s):  
Random Permutations ◽  
Longest Increasing Subsequence

scholarly journals Random Permutations, Non-Decreasing Subsequences and Statistical Independence

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1415
Author(s):  
Jesús E. García ◽  
Verónica A. González-López
Keyword(s):  
Random Variables ◽  
Continuous Data ◽  
Random Permutations ◽  
Statistical Independence ◽  
Independence Test ◽  
Independence Tests ◽  
Present Procedure ◽  
Longest Increasing Subsequence

In this paper, we show how the longest non-decreasing subsequence, identified in the graph of the paired marginal ranks of the observations, allows the construction of a statistic for the development of an independence test in bivariate vectors. The test works in the case of discrete and continuous data. Since the present procedure does not require the continuity of the variables, it expands the proposal introduced in Independence tests for continuous random variables based on the longest increasing subsequence (2014). We show the efficiency of the procedure in detecting dependence in real cases and through simulations.

scholarly journals Longest Alternating Subsequences in Pattern-Restricted Permutations

10.37236/952 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Ghassan Firro ◽  
Toufik Mansour ◽  
Mark C. Wilson
Keyword(s):  
Generating Functions ◽  
Complex Analysis ◽  
Limiting Distribution ◽  
Future Research ◽  
Random Permutations ◽  
Restricted Permutations ◽  
Longest Increasing Subsequence

Inspired by the results of Stanley and Widom concerning the limiting distribution of the lengths of longest alternating subsequences in random permutations, and results of Deutsch, Hildebrand and Wilf on the limiting distribution of the longest increasing subsequence for pattern-restricted permutations, we find the limiting distribution of the longest alternating subsequence for pattern-restricted permutations in which the pattern is any one of the six patterns of length three. Our methodology uses recurrences, generating functions, and complex analysis, and also yields more detailed information. Several ideas for future research are listed.

scholarly journals Longest Increasing Subsequences of Random Colored Permutations

10.37236/1445 ◽  
1999 ◽  
Vol 6 (1) ◽  
Author(s):  
Alexei Borodin
Keyword(s):  
Distribution Function ◽  
Limit Distribution ◽  
Main Idea ◽  
Random Permutations ◽  
Signed Permutations ◽  
Limit Distribution Function ◽  
Longest Increasing Subsequence ◽  
Colored Permutations

We compute the limit distribution for the (centered and scaled) length of the longest increasing subsequence of random colored permutations. The limit distribution function is a power of that for usual random permutations computed recently by Baik, Deift, and Johansson (math.CO/9810105). In the two–colored case our method provides a different proof of a similar result by Tracy and Widom about the longest increasing subsequences of signed permutations (math.CO/9811154). Our main idea is to reduce the 'colored' problem to the case of usual random permutations using certain combinatorial results and elementary probabilistic arguments.

Isn't it eyeronic? Little evidence for consistent eye colour choices across relationships

2018 ◽  
Author(s):  
Amy Victoria Newman ◽  
Thomas V. Pollet ◽  
Kristofor McCarty ◽  
Nick Neave ◽  
Tamsin Saxton
Keyword(s):  
Good Evidence ◽  
Random Permutations ◽  
Three Samples ◽  
Eye Colour ◽  
A Priority

This study examined the anecdotal notion that people choose partners based on preferred characteristics that constitute their ‘type’. We gathered the eye colours of participants’ partners across their entire romantic history in three samples (student-centred, adult, and celebrity). We calculated the proportion of partners’ eye colours, and compared that to 100,000 random permutations of our observed dataset using t-tests. This was to investigate if the eye colour choices in the original datasets had greater consistency than in the permutations. Across all samples, we observed no good evidence that individuals make consistent eye colour choices, suggesting that eye colour may not be a priority when choosing a partner.

scholarly journals Permutations with equal orders

2021 ◽  
pp. 1-11
Author(s):  
Huseyin Acan ◽  
Charles Burnette ◽  
Sean Eberhard ◽  
Eric Schmutz ◽  
James Thomas
Keyword(s):  
Random Permutations

Abstract Let ${\mathbb{P}}(ord\pi = ord\pi ')$ be the probability that two independent, uniformly random permutations of [n] have the same order. Answering a question of Thibault Godin, we prove that ${\mathbb{P}}(ord\pi = ord\pi ') = {n^{ - 2 + o(1)}}$ and that ${\mathbb{P}}(ord\pi = ord\pi ') \ge {1 \over 2}{n^{ - 2}}lg*n$ for infinitely many n. (Here lg*n is the height of the tallest tower of twos that is less than or equal to n.)

scholarly journals Exact testing with random permutations

Test ◽  
2017 ◽  
Vol 27 (4) ◽  
pp. 811-825 ◽  
Author(s):  
Jesse Hemerik ◽  
Jelle Goeman
Keyword(s):  
Random Permutations
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