scholarly journals Longest Increasing Subsequence Under Persistent Comparison Errors

2018 ◽  
pp. 259-276
Author(s):  
Barbara Geissmann
Keyword(s):  
Longest Increasing Subsequence

scholarly journals What do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know About Each Other?

2019 ◽  
Author(s):  
Elizabeth J. Itskovich ◽  
Vadim E. Levit
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Longest Increasing Subsequence ◽  
Necessary And Sufficient

As a kind of converse of the celebrated Erd˝os-Szekeres theorem, we present a necessary and sufficient condition for a sequence of length n to contain a longest increasing subsequence and a longest decreasing subsequence of given lengths x and y, respectively.

scholarly journals Space-Efficient Algorithms for Longest Increasing Subsequence

2019 ◽  
Vol 64 (3) ◽  
pp. 522-541
Author(s):  
Masashi Kiyomi ◽  
Hirotaka Ono ◽  
Yota Otachi ◽  
Pascal Schweitzer ◽  
Jun Tarui
Keyword(s):  
Efficient Algorithms ◽  
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 Permutations Without Long Decreasing Subsequences and Random Matrices

10.37236/929 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Piotr Šniady
Keyword(s):  
Random Matrices ◽  
Young Diagram ◽  
Random Matrix ◽  
Random Permutation ◽  
Fixed Number ◽  
Plancherel Measure ◽  
Young Diagrams ◽  
Gaussian Unitary Ensemble ◽  
Longest Increasing Subsequence ◽  
Unitary Ensemble

We study the shape of the Young diagram $\lambda$ associated via the Robinson–Schensted–Knuth algorithm to a random permutation in $S_n$ such that the length of the longest decreasing subsequence is not bigger than a fixed number $d$; in other words we study the restriction of the Plancherel measure to Young diagrams with at most $d$ rows. We prove that in the limit $n\to\infty$ the rows of $\lambda$ behave like the eigenvalues of a certain random matrix (namely the traceless Gaussian Unitary Ensemble random matrix) with $d$ rows and columns. In particular, the length of the longest increasing subsequence of such a random permutation behaves asymptotically like the largest eigenvalue of the corresponding random matrix.

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