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Adjacencies in Permutations
[article]

2016
*
arXiv
*
pre-print

We denote the set of

arXiv:1601.04469v1
fatcat:frqzxy5q5jcc7buchqxsjpfak4
*permutations**in*P_n with exactly k*adjacencies*with P_n (k). ... The concept of*adjacencies*is widely used*in*computation. The set of*permutations*over Σ forms a symmetric group, that we call P _n . The identity*permutation*, I _n ∈ P_n where I_n =(0,1,2,... ... P n (k) denotes the set of*permutations**in*P n with exactly k*adjacencies*; the type of*adjacency*will be evident from the context. We compute ∀k |P n (k)|*in*O(n 2 ) time for any type of*adjacency*. ...##
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Adjacent q-cycles in permutations
[article]

2010
*
arXiv
*
pre-print

We introduce a new

arXiv:1005.0781v2
fatcat:65bvm7rkvvc4rnornwbaaesmei
*permutation*statistic, namely, the number of cycles of length q consisting of consecutive integers, and consider the distribution of this statistic among the*permutations*of {1,2,... ...*Adjacent*cycles of more than one length Up to now we have considered*permutations*focusing on*adjacent*cycles of one given length q. ...*In*Section 5, we obtain a formula for the number of*permutations*having a specified number of*adjacent*cycles of each of several lengths. ...##
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A Permutation Test for Correlated Errors in Adjacent Questionnaire Items

2013
*
Structural Equation Modeling
*

This pattern manifests itself

doi:10.1080/10705511.2013.769390
fatcat:ff24ljfpx5boxamf2nypladzl4
*in*the error structure of the survey items by resulting*in*larger correlations of the errors for*adjacent*items than for nonadjacent items. ...*In*this paper we propose the use of structural equation modeling to examine response patterns and develop a*permutation*test to quantify the likelihood of observing a specific response pattern. ... The results for the*permutation*test are displayed*in*Figure 3 . ...##
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Is There a Sequence on Four Symbols in Which No Two Adjacent Segments are Permutations of One Another?

1971
*
The American mathematical monthly
*

Then

doi:10.1080/00029890.1971.11992892
fatcat:ce6rnto2cfbzpkljxyx6n3qk5u
*in*1970 a paper appeared [13]*in*which P. A. B. Pleasants gave a construction of a sequence on 5 symbols without 2nd powers mod α. ... The segments s[i + 1; j] and s[p + 1; q] are identically equal if k i = q p and x i+1 = x p+1 ; x i+2 = x p+2 ; : : : ; x k = x q or,*in*other words, if s[i + 1; k] = s[p + 1; q]*in*X £ , the free semigroup ... Klee for drawing attention to the references*in*a draft by H. T. Croft and R. K. Guy of their forthcoming book Research Problems*in*Intuitive Mathematics. ...##
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Impact of Downlink Distributed and Adjacent Subcarrier Permutation Modes on the Performance of Mobile WiMAX System in ITU-R Ped. B Channel with Obtaining Optimum Cyclic Prefix

2012
*
Al-Rafidain Engineering Journal
*

*In*this paper the impact of downlink distributed (FUSC, PUSC) and

*adjacent*(AMC) subcarrier

*permutation*modes used

*in*mobile WiMAX system are investigated using simulation under various modulation and ... The results show the optimum cyclic prefix valve for the FUSC, PUSC and AMC subcarrier

*permutation*modes to achieve the best system performance, also the results show differences

*in*PER performance atvarious ... Diversity

*permutations*minimize the probability of using the same subcarrier

*in*

*adjacent*sectors or cells. ...

##
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Adjacent transformations in permutations

2011
*
FPSAC 2011, Reykjavík, Iceland DMTCS proc. AO
*
unpublished

We continue a study of the equivalence class induced on Sn when one is permitted to replace a consecutive set of elements

fatcat:4hgbr3gah5gd5jbnmzeeat6t4y
*in*a*permutation*with the same elements*in*a different order. ... For each possible set of allowed replacements , we characterise and/or enumerate the set of*permutations*reachable from the identity.*In*some cases we also count the number of equivalence classes. ...*in*equivalence classes of size 1 as isolated*permutations*. ...##
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Progress in Adjacent Vertex Distinguishing (Avd) Edge Colouring of Permutation Graphs

2015
*
Progress in Nonlinear Dynamics and Chaos
*
unpublished

*Adjacent*vertex distinguishing edge coloring (avd edge colouring

*in*short) applied on different type of

*permutation*graphs. ... A graph G=(V,E) with vertex set on N, the set of natural numbers is called a

*permutation*graph if there exists a

*permutation*= {(1),(2),... ...

*Adjacent*Vertex Distinguishing (Avd) Edge Colouring of

*Permutation*Graphs 11 Geometrically, the integers 1,2,3,…,n are drawn

*in*order on a real line called an upper line and ߨ(1), ߨ(2),…, ߨ(n) on a line ...

##
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On the Möbius Function of Permutations With One Descent
[article]

2014
*
arXiv
*
pre-print

The set of all

arXiv:1306.5926v3
fatcat:um3m3brgrzgq3jdmqmyurvfqqa
*permutations*, ordered by pattern containment, is a poset. We give a formula for the Möbius function of intervals [1,π]*in*this poset, for any*permutation*π with at most one descent. ... We compute the Möbius function as a function of the number and positions of pairs of consecutive letters*in*π that are consecutive*in*value. ... and pointing out an error, now fixed,*in*Lemma 8. ...##
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Intervals of permutations and the principal Möbius function
[article]

2018
*
arXiv
*
pre-print

We also show that if a

arXiv:1806.10362v2
fatcat:jgx6hzd3jzfo5agmhls2vxgb5m
*permutation*ϕ has certain properties, then any*permutation*π which contains an interval order-isomorphic to ϕ has μ[1, π] = 0. ... We show that the proportion of*permutations*of length n with principal Möbius function equal to zero, Z(n), is asymptotically bounded below by 0.3995. ... Acknowledgements The computations*in*Section 5 were performed using Maple TM [8] . ...##
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Correcting adjacent errors using permutation code trees

2011
*
IEEE Africon '11
*

*In*this paper, we show that, due to the structure of the

*permutation*code tree,

*adjacent*errors can also be corrected if the codebook is adapted. ...

*Permutation*codes are M-ary codes which can be used,

*in*combination with M-ary FSK, to correct errors

*in*Power Line Communications (PLC). ... The

*permutation*code tree can also correct a combination of single and

*adjacent*errors. The codebooks

*in*[1] need to be adjusted to accommodate

*adjacent*errors. ...

##
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A tight upper bound on the number of cyclically adjacent transpositions to sort a permutation

2016
*
Information Processing Letters
*

It is well known that any

doi:10.1016/j.ipl.2016.06.006
fatcat:owu75adzhvgejdnfqkvx6osbkm
*permutation*can be sorted using at most n(n−1) 2*adjacent*transpositions. ... We show that, if we allow all*adjacent*transpositions, as well as the transposition that interchanges the element*in*position 1 with the element*in*the last position, then the number of transpositions ... Let π be a*permutation*of S, and let Q = (q 1 , q 2 , . . . , q m ) be a sequence of cyclically*adjacent*swaps for π, resulting*in**permutation*σ. ...##
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Topological crossover for the permutation representation

2005
*
Proceedings of the 2005 workshops on Genetic and evolutionary computation - GECCO '05
*

*In*this paper we explore how the topological framework applies to the

*permutation*representation and

*in*particular analyse the consequences of having more than one notion of distance available. ... Also, we study the interactions among distances and build a rational picture

*in*which pre-existing recombination/crossover operators for

*permutation*fit naturally. ...

*adjacency*relation of the elements

*in*the

*permutation*. ...

##
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Error-correcting codes for rank modulation

2008
*
2008 IEEE International Symposium on Information Theory
*

*In*this scheme, a set of n cells stores information

*in*the

*permutation*induced by the different charge levels of the individual cells. ... We show that the

*adjacency*graph of

*permutations*is a subgraph of a multi-dimensional array of a special size, a property that enables code designs based on Leemetric codes. ... Proof: Let A and B be two

*permutations*such that X A and X B are

*adjacent*

*in*L n . If they are not

*adjacent*

*permutations*, then they must violate condition 2

*in*Theorem 4. ...

##
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An Upper Bound on the Number of Circular Transpositions to Sort a Permutation
[article]

2014
*
arXiv
*
pre-print

It is well known that any

arXiv:1402.4867v1
fatcat:y352bmohnbfvxl6mjhpy5dmdpe
*permutation*can be sorted using at most n(n-1)/2*adjacent*transpositions. ... We show that, if we allow all*adjacent*transpositions, as well as the transposition that interchanges the element*in*position 1 with the element*in*the last position, then the number of transpositions ... Let π be a*permutation*of S, and let Q = (q 1 , q 2 , . . . , q m ) be a sequence of cyclically*adjacent*swaps for π, resulting*in**permutation*σ. ...##
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Short proofs for cut-and-paste sorting of permutations

2007
*
Discrete Mathematics
*

We give short proofs that every

doi:10.1016/j.disc.2007.01.011
fatcat:juyeltrayrf2zawsacgvwgdryy
*permutation*of [n] can be transformed to the identity*in*at most 2n/3 such moves and that some*permutations*require at least n/2 moves. ... We consider the problem of determining the maximum number of moves required to sort a*permutation*of [n] using cut-and-paste operations,*in*which a segment is cut out and then pasted into the remaining ... The proof*in*fact shows that every input*permutation*with one parity*adjacency*(when n is even) or two parity*adjacencies*(when n is odd) requires n/2 moves to sort. ...
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