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| 2. |
- Schellwat, Holger
(författare)
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Induced Cayley graphs and double covers
- 1995
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Ingår i: Linear and multilinear algebra. - 0308-1087 .- 1563-5139. ; 39:1-2, s. 161-164
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Tidskriftsartikel (refereegranskat)
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| 3. |
- Eriksen, Niklas, 1974-, et al.
(författare)
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Equidistributed Statistics on Matchings and Permutations
- 2014
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Ingår i: The Electronic Journal of Combinatorics. - : The Electronic Journal of Combinatorics. - 1097-1440 .- 1077-8926. ; 21:4
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Tidskriftsartikel (refereegranskat)abstract
- We show that the bistatistic of right nestings and right crossings in matchings without left nestings is equidistributed with the number of occurrences of two certain patterns in permutations, and furthermore that this equidistribution holds when refined to positions of these statistics in matchings and permutations. For this distribution we obtain a non-commutative generating function which specializes to Zagier's generating function for the Fishburn numbers after abelianization. As a special case we obtain proofs of two conjectures of Claesson and Linusson. Finally, we conjecture that our results can be generalized to involving left crossings of matchings too.
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| 4. |
- Eriksen, Niklas, 1974-
(författare)
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Expected number of breakpoints after t random reversals in genomes with duplicate genes
- 2008
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Ingår i: Discrete Applied Mathematics. - Amsterdam, Netherlands : Elsevier. - 0166-218X .- 1872-6771. ; 156:12, s. 2320-2335
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Tidskriftsartikel (refereegranskat)abstract
- In comparative genomics, one wishes to deduce the evolutionary distance between different species by studying their genomes. Using gene order information, we seek the number of times the gene order has changed between two species. One approach is to compute the method of moments estimate of this edit distance from a measure of dissimilarity called the breakpoint measure. In this paper, we extend formulae and bounds of this estimate on gene permutations to genomes with duplicate genes.
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| 5. |
- Eriksen, Niklas, 1974
(författare)
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Reversal and Transposition Medians
- 2007
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Ingår i: Theoretical Computer Science. - Amsterdam, Netherlands : Elsevier. ; 374:1-3, s. 111-126
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Tidskriftsartikel (refereegranskat)abstract
- In determining phylogenetic trees using gene order information, medians provide a powerful alternative to pairwise distances. On the other hand, both breakpoint and reversal medians are NP-hard to compute and the use of medians has been limited to relatively closely related genomes. In this paper, we show that in spite of the greater non-uniqueness of reversal medians, compared to breakpoint medians, medians of moderately distant genomes are often widely spread. This means that regardless of which approximation algorithms one may devise for computing reversal medians, the genomes need to be closely related for phylogenetic tree computations to be successful. To show this, we use results on transposition medians, which behave similarly, and also support our claims with simulations and a real data example with widely spread medians.
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| 6. |
- Eriksen, Niklas, 1974, et al.
(författare)
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Enumeration of derangements with descents in prescribed positions
- 2009
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Ingår i: Electronic Journal of Combinatorics. - : The Electronic Journal of Combinatorics. - 1077-8926 .- 1097-1440. ; 16:1
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Tidskriftsartikel (refereegranskat)abstract
- We enumerate derangements with descents in prescribed positions. A generating function was given by Guo-Niu Han and Guoce Xin in 2007. We give a combinatorial proof of this result, and derive several explicit formulas. To this end, we consider fixed point $\lambda$-coloured permutations, which are easily enumerated. Several formulae regarding these numbers are given, as well as a generalisation of Euler's difference tables. We also prove that except in a trivial special case, if a permutation $\pi$ is chosen uniformly among all permutations on $n$ elements, the events that $\pi$ has descents in a set $S$ of positions, and that $\pi$ is a derangement, are positively correlated.
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| 7. |
- Schellwat, Holger, 1959-
(författare)
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A Gentle Introduction to a Beautiful Theorem of Molien
- 2017
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Rapport (populärvet., debatt m.m.)abstract
- The purpose of this note is to give an accessible proof of Moliens Theorem in Invariant Theory, in the language of today's Linear Algebra and Group Theory, in order to prevent this beautiful theorem from being forgotten.
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| 8. |
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| 9. |
- Dalevi, Daniel, 1974, et al.
(författare)
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Expected Gene Order Distances and Model Selection in Bacteria
- 2008
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Ingår i: Bioinformatics. - Oxford, United Kingdom : Oxford University Press. - 1367-4803 .- 1367-4811. ; 24:11, s. 1332-1338
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Tidskriftsartikel (refereegranskat)abstract
- Motivation: The evolutionary distance inferred from gene-order comparisons of related bacteria is dependent on the model. Therefore, it is highly important to establish reliable assumptions before inferring its magnitude. Results: We investigate the patterns of dotplots between species of bacteria with the purpose of model selection in gene-order problems. We find several categories of data which can be explained by carefully weighing the contributions of reversals, transpositions, symmetrical reversals, single gene transpositions and single gene reversals. We also derive method of moments distance estimates for some previously uncomputed cases, such as symmetrical reversals, single gene reversals and their combinations, as well as the single gene transpositions edit distance.
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| 10. |
- Eriksen, Niklas, 1974-
(författare)
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Approximating the expected number of inversions given the number of breakpoints
- 2002
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Ingår i: Lecture Notes in Computer Science. - Berlin, Germany : Springer Berlin/Heidelberg. - 0302-9743 .- 1611-3349. - 3540442111 ; 2452, s. 316-330
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Tidskriftsartikel (refereegranskat)abstract
- We look at a problem with motivation from computational biology: Given the number of breakpoints in a permutation (representing a gene sequence), compute the expected number of inversions that have occured. For this problem, we obtain an analytic approximation that is correct within a percent or two. For the inverse problem, computing the expected number of breakpoints after any number of inversions, we obtain an analytic approximation with an error of less than a hundredth of a breakpoint.
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