A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Minimum Number of Monotone Subsequences of Length 4 in Permutations

2014
*
Combinatorics, probability & computing
*

We show that for every sufficiently largen, the

doi:10.1017/s0963548314000820
fatcat:6rh274ecujdhffngmkly34z22u
*number**of**monotone**subsequences**of**length*four*in*a*permutation*onnpoints is at least\begin{equation*} \binom{\lfloor{n/3}\rfloor}{*4*} + \binom{\lfloor{(n ... This translates back to*permutations*, where all the*monotone**subsequences**of**length*four are all either increasing, or decreasing only. ... Acknowledgement We would like to thank Dan Krá , l for fruitful discussions and developing the first version*of*the program implementing flag algebras over*permutations*. ...##
###
The Minimum Number of Monotone Subsequences

2002
*
Electronic Journal of Combinatorics
*

Erdős and Szekeres showed that any

doi:10.37236/1676
fatcat:y3rl5xf2kzdeffrk2lbzbqwf7m
*permutation**of**length*$n \geq k^2+1$ contains a*monotone**subsequence**of**length*$k+1$. ... For $k > 2$ and $n \geq k(2k-1)$, we characterise the*permutations*containing the*minimum**number**of**monotone**subsequences**of**length*$k+1$ subject to the additional constraint that all such*subsequences*... We write m k (S) for the*number**of**monotone**subsequences**of**length*k + 1*in*the*permutation*S. ...##
###
Page 7609 of Mathematical Reviews Vol. , Issue 2004j
[page]

2004
*
Mathematical Reviews
*

7609
2004j:05008 05A05 05D99
Myers, Joseph Samuel (

*4*-CAMB-CM; Cambridge) The*minimum**number**of**monotone**subsequences*. (English summary)*Permutation*patterns (Otago, 2003). Electron. J. ... There is also some computa- tional evidence to support the conjecture that all*permutations**of**length*» with n > k(2k —1) and a*minimum**number**of**monotone**subsequences**of**length*A +1, must have all such ...##
###
On minimum k-modal partitions of permutations

2008
*
Journal of Discrete Algorithms
*

Partitioning a

doi:10.1016/j.jda.2008.01.002
fatcat:xpik3ui5znfxbcux2tje2pmd3m
*permutation*into a*minimum**number**of**monotone**subsequences*is N P-hard. ... For the online problem,*in*which the*permutation*becomes known to an algorithm sequentially, we derive a logarithmic lower bound on the competitive ratio for*minimum**monotone*partitions, and we analyze ...*In*particular for 1-modal, or unimodal,*subsequences*Chung [5] proves that any*permutation**of**length*n contains such a*subsequence**of**length*√ 3(n − 1/*4*) − 1/2 , and this is best possible. ...##
###
On Minimum k-Modal Partitions of Permutations
[chapter]

2006
*
Lecture Notes in Computer Science
*

Partitioning a

doi:10.1007/11682462_36
fatcat:yi3v5dw6mzgyji2nw5echeqb3u
*permutation*into a*minimum**number**of**monotone**subsequences*is N P-hard. ... For the online problem,*in*which the*permutation*becomes known to an algorithm sequentially, we derive a logarithmic lower bound on the competitive ratio for*minimum**monotone*partitions, and we analyze ...*In*particular for 1-modal, or unimodal,*subsequences*Chung [5] proves that any*permutation**of**length*n contains such a*subsequence**of**length*√ 3(n − 1/*4*) − 1/2 , and this is best possible. ...##
###
Crucial and bicrucial permutations with respect to arithmetic monotone patterns
[article]

2012
*
arXiv
*
pre-print

A pattern τ is a

arXiv:1210.2621v1
fatcat:qmkjgj54nrditcqjfevd3fzgdq
*permutation*, and an arithmetic occurrence*of*τ*in*(another)*permutation*π=π_1π_2...π_n is a*subsequence*π_i_1π_i_2...π_i_m*of*π that is order isomorphic to τ where the*numbers*i_1<i_2< ... Moreover, we show that the minimal*length**of*a (k,ℓ)-crucial*permutation*is (k,ℓ)((k,ℓ)-1), while the minimal*length**of*a (k,ℓ)-bicrucial*permutation*is at most 2(k,ℓ)((k,ℓ)-1), again for k,ℓ≥3. ...*monotone**subsequences**of**length**4*or more can have at most one large white element and one small white element leading to the fact that a*monotone**subsequence**of*the*permutation**in*Figure 6 are*of**length*...##
###
An Erdős--Hajnal analogue for permutation classes
[article]

2016
*
arXiv
*
pre-print

We prove that there is a constant c such that every

arXiv:1511.01076v2
fatcat:zvqtnykvfnbkbk5ihs4euuabae
*permutation**in*C*of**length*n contains a*monotone**subsequence**of**length*cn. ... Let C be a*permutation*class that does not contain all layered*permutations*or all colayered*permutations*. ... There is a constant c > 0 such that every*permutation**of**length*n*in*C contains a*monotone**subsequence**of**length*at least cn. One special case*of*Theorem 1 is quite easy. ...##
###
Avoidance of boxed mesh patterns on permutations

2013
*
Discrete Applied Mathematics
*

Finally, we discuss enumeration

doi:10.1016/j.dam.2012.08.015
fatcat:gsdyihucfzetnky4trw647nkfm
*of**permutations*avoiding simultaneously two or more*length*-three boxed mesh patterns, where we meet generalized Catalan*numbers*. ... We introduce the notion*of*a boxed mesh pattern and study avoidance*of*these patterns on*permutations*. ... The third author was also supported by the grant*of*the President*of*the Russian Federation for Young Russian researchers (project no. MK-4075.2012.1) ...##
###
A quadratic time 2-approximation algorithm for block sorting

2009
*
Theoretical Computer Science
*

The block sorting problem is the problem

doi:10.1016/j.tcs.2008.10.022
fatcat:zho2rjgxireghodcuy6mskg4oe
*of*minimizing the*number**of*steps to sort a list*of*distinct items, where a sublist*of*items which are already*in*sorted order, called a block, can be moved*in*... Block sorting has importance*in*connection with optical character recognition (OCR) and is related to transposition sorting*in*computational biology. ... This author worked on this project at the University*of*Texas at Dallas while on sabbatical leave from UNLV. Second author is supported by NSF grant CCR-0312093. ...##
###
On compressing permutations and adaptive sorting

2013
*
Theoretical Computer Science
*

We prove that, given a

doi:10.1016/j.tcs.2013.10.019
fatcat:vxgaveeqkbhtdeuhbtfcczeery
*permutation*π over [1..n] formed*of*nRuns sorted blocks*of*sizes given by the vector R = r 1 , . . . , r nRuns , there exists a compressed data structure encoding n r i n(1 + log ... 2 nRuns) bits while supporting access to the values*of*π () and π −1 ()*in*time O(log nRuns/ log log n)*in*the worst case and O(H(R)/ log log n) on average, when the argument is uniformly distributed ... on them based on optimality implications*in*terms*of*the*number**of*comparisons performed. ...##
###
Generalised Pattern Avoidance
[article]

2000
*
arXiv
*
pre-print

We consider pattern avoidance for such patterns, and give a complete solution for the

arXiv:math/0011235v1
fatcat:zilhpaytb5ebbplz47ogoywglu
*number**of**permutations*avoiding any single pattern*of**length*three with exactly one adjacent pair*of*letters. ... We also give some results for the*number**of**permutations*avoiding two different patterns. ... Acknowledgement I am greatly indebted to my advisor Einar Steingrímsson, who put his trust*in*me and gave me the opportunity to study mathematics on a postgraduate level. ...##
###
Two RPG Flow-graphs for Software Watermarking using Bitonic Sequences of Self-inverting Permutations
[article]

2016
*
arXiv
*
pre-print

Following up on our recently proposed methods for encoding watermark

arXiv:1607.02281v2
fatcat:ljefcwmiozb7ppjbsr3gndcxwy
*numbers*w as reducible*permutation*flow-graphs F[π^*] through the use*of*self-inverting*permutations*π^*,*in*this paper, we extend the ... bitonic*subsequences*composing the self-inverting*permutation*π^*. ...*In*this paper, we consider only bitonic sequences that*monotonically*increases and then*monotonically*decreases, i.e., the*minimum*element*of*such a sequence b is either the first b 1 or the last b n element ...##
###
Upper Bound Constructions for Untangling Planar Geometric Graphs

2014
*
SIAM Journal on Discrete Mathematics
*

as

doi:10.1137/130924172
fatcat:mvpohhbiyrbmpcxzlkutnzzfie
*in*Dn. ... For every n ∈ N, there is a straight-line drawing Dn*of*a planar graph on n vertices such that*in*any crossing-free straight-line drawing*of*the graph, at most O(n .4982 ) vertices lie at the same position ... By Lemma 1, the spread*of*the*monotone**subsequence**of**length*at least i /*4*is at least ( 2 i + 32)/96. Hence these fixed points "occupy" an interval*of**length*( 2 i + 32)/96 on the x-axis. ...##
###
Upper Bound Constructions for Untangling Planar Geometric Graphs
[chapter]

2012
*
Lecture Notes in Computer Science
*

as

doi:10.1007/978-3-642-25878-7_28
fatcat:l3tn3jiufvfxndwtcxlrhkocj4
*in*Dn. ... For every n ∈ N, there is a straight-line drawing Dn*of*a planar graph on n vertices such that*in*any crossing-free straight-line drawing*of*the graph, at most O(n .4982 ) vertices lie at the same position ... By Lemma 1, the spread*of*the*monotone**subsequence**of**length*at least i /*4*is at least ( 2 i + 32)/96. Hence these fixed points "occupy" an interval*of**length*( 2 i + 32)/96 on the x-axis. ...##
###
Generalized Pattern Avoidance

2001
*
European journal of combinatorics (Print)
*

We will consider pattern avoidance for such patterns, and give a complete solution for the

doi:10.1006/eujc.2001.0515
fatcat:q43shpidzfftdaqlkgd2nldqeu
*number**of**permutations*avoiding any single pattern*of**length*three with exactly one adjacent pair*of*letters. ... We also give some results for the*number**of**permutations*avoiding two different patterns. ... Acknowledgement I am greatly indebted to my advisor Einar Steingrímsson, who put his trust*in*me and gave me the opportunity to study mathematics on a postgraduate level. ...
« Previous

*Showing results 1 — 15 out of 14,544 results*