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Adjacencies in Permutations [article]

Bhadrachalam Chitturi, Krishnaveni K S
2016 arXiv   pre-print
We denote the set of 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.  ... 
arXiv:1601.04469v1 fatcat:frqzxy5q5jcc7buchqxsjpfak4

Adjacent q-cycles in permutations [article]

Richard A. Brualdi, Emeric Deutsch
2010 arXiv   pre-print
We introduce a new 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.  ... 
arXiv:1005.0781v2 fatcat:65bvm7rkvvc4rnornwbaaesmei

A Permutation Test for Correlated Errors in Adjacent Questionnaire Items

Laura A. Hildreth, Ulrike Genschel, Frederick O. Lorenz, Virginia M. Lesser
2013 Structural Equation Modeling  
This pattern manifests itself 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 .  ... 
doi:10.1080/10705511.2013.769390 fatcat:ff24ljfpx5boxamf2nypladzl4

Is There a Sequence on Four Symbols in Which No Two Adjacent Segments are Permutations of One Another?

T. C. Brown
1971 The American mathematical monthly  
Then 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.  ... 
doi:10.1080/00029890.1971.11992892 fatcat:ce6rnto2cfbzpkljxyx6n3qk5u

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

Safwan E. Abdul Fatah, Dr. Sami A. Mawjoud
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.  ... 
doi:10.33899/rengj.2012.54157 fatcat:vipdprsjqbbphb2nztb2ocg7y4

Adjacent transformations in permutations

Adeline Pierrot, Dominique Rossin, Julian West
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 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.  ... 
fatcat:4hgbr3gah5gd5jbnmzeeat6t4y

Progress in Adjacent Vertex Distinguishing (Avd) Edge Colouring of Permutation Graphs

Suparna Jana
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  ... 
fatcat:3rznxfiz7bhkle4vwsj5sllavq

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

Jason P Smith
2014 arXiv   pre-print
The set of all 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.  ... 
arXiv:1306.5926v3 fatcat:um3m3brgrzgq3jdmqmyurvfqqa

Intervals of permutations and the principal Möbius function [article]

Robert Brignall, David Marchant
2018 arXiv   pre-print
We also show that if a 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] .  ... 
arXiv:1806.10362v2 fatcat:jgx6hzd3jzfo5agmhls2vxgb5m

Correcting adjacent errors using permutation code trees

R. Heymann, T.G. Swart, H.C. Ferreira
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.  ... 
doi:10.1109/afrcon.2011.6072122 fatcat:d7qdykt4wzb4tdas5l365la7zy

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

Anke van Zuylen, James Bieron, Frans Schalekamp, Gexin Yu
2016 Information Processing Letters  
It is well known that any 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.  ... 
doi:10.1016/j.ipl.2016.06.006 fatcat:owu75adzhvgejdnfqkvx6osbkm

Topological crossover for the permutation representation

Alberto Moraglio, Riccardo Poli
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.  ... 
doi:10.1145/1102256.1102330 dblp:conf/gecco/MoraglioP05 fatcat:rass45w3ejfy5bxjk5i66dcosa

Error-correcting codes for rank modulation

Anxiao Jiang, Moshe Schwartz, Jehoshua Bruck
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.  ... 
doi:10.1109/isit.2008.4595285 dblp:conf/isit/JiangSB08 fatcat:czbhgcsrb5bhnb2xwsg4e7cqvy

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

Anke van Zuylen, James Bieron, Frans Schalekamp, Gexin Yu
2014 arXiv   pre-print
It is well known that any 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.  ... 
arXiv:1402.4867v1 fatcat:y352bmohnbfvxl6mjhpy5dmdpe

Short proofs for cut-and-paste sorting of permutations

Daniel W. Cranston, I. Hal Sudborough, Douglas B. West
2007 Discrete Mathematics  
We give short proofs that every 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.  ... 
doi:10.1016/j.disc.2007.01.011 fatcat:juyeltrayrf2zawsacgvwgdryy
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