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| 2. |
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| 3. |
- Brattström, Gudrun
(författare)
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Leonardo da Pisa : Inger Christensen och Fibonacci
- 2008
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Ingår i: Lyrikvännen. - 0460-0762. ; 55:6, s. 33-38
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Tidskriftsartikel (populärvet., debatt m.m.)abstract
- Den danska poeten Inger Christensen byggde sin diktsamling Alfabet på Fibonaccis talserie. Artikeln är en kort historisk essä över Fibonacci, och beskriver även hur talserien är konstruerad.
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| 4. |
- Asratian, Armen, et al.
(författare)
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Proper path-factors and interval edge-coloring of (3,4)-biregular bigraphs
- 2009
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Ingår i: Journal of Graph Theory. - : Wiley Periodicals Inc.. - 0364-9024 .- 1097-0118. ; 61:2, s. 88-97
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Tidskriftsartikel (refereegranskat)abstract
- An interval coloring of a graph G is a proper coloring of E(G) by positive integers such that the colors on the edges incident to any vertex are consecutive. A (3,4)-biregular bigraph is a bipartite graph in which each vertex of one part has degree 3 and each vertex of the other has degree 4; it is unknown whether these all have interval colorings. We prove that G has an interval coloring using 6 colors when G is a (3,4)-biregular bigraph having a spanning subgraph whose components are paths with endpoints at 3-valent vertices and lengths in {2, 4, 6, 8}. We provide several sufficient conditions for the existence of such a subgraph.
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| 5. |
- Brändén, Petter, 1976
(författare)
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Counterexamples to the Neggers-Stanley conjecture
- 2004
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Ingår i: Electronic Research Announcements of the American Mathematical Society. - 1079-6762. ; 10, s. 155-158
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Annan publikation (övrigt vetenskapligt/konstnärligt)
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| 6. |
- 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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| 7. |
- 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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| 8. |
- 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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| 9. |
- Eriksen, Niklas, 1974
(författare)
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The freshman's approach to Conway's napkin problem
- 2008
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Ingår i: The American mathematical monthly. - Washington, USA : Mathematical Association of America. - 0002-9890 .- 1930-0972. ; 115:6, s. 492-498
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Tidskriftsartikel (refereegranskat)abstract
- In the March 2006 issue of the MONTHLY, Claesson and Petersen gave a thorough solution to Conway's napkin problem. The problem is the following: Assume that n mathematicians arrive in random order at a conference dinner with a circular table, and that the napkins are placed exactly halfway between the plates so that the guests do not know whether they are supposed to use the right or the left napkin. Each guest prefers these napkins with probabilities p and 1-p, respectively, and tries her preferred alternative before trying the other, if the preferred napkin has been taken. Which proportion of guests is expected to sit down at a place where both adjacent napkins have been taken and thus be without a napkin? Claesson and Petersen use a system of generating functions to compute both the expectation and the variance of this proportion and to address similar questions, for instance regarding the number of guests who get a napkin though not the preferred one. However, these expectations can also be computed using purely elementary methods, such as the binomial theorem. We present the freshman's approach to the napkin problem and related problems, for instance the one with French diners mentioned, but not solved, by Claesson and Petersen.
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| 10. |
- Hultman, Axel, et al.
(författare)
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From Bruhat intervals to intersection lattices and a conjecture of Postnikov
- 2009
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Ingår i: Journal of combinatorial theory. Series A (Print). - : Elsevier BV. - 0097-3165 .- 1096-0899. ; 116:3, s. 564-580
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Tidskriftsartikel (refereegranskat)abstract
- We prove the conjecture of A. Postnikov that (A) the number of regions in the inversion hyperplane arrangement associated with a permutation w is an element of (sic)(n). is at most the number of elements below w in the Bruhat order, and (B) that equality holds if and only if w avoids the patterns 4231, 35142, 42513 and 351624. Furthermore, assertion (A) is extended to all finite reflection groups. A byproduct of this result and its proof is a set of inequalities relating Betti numbers of complexified inversion arrangements to Betti numbers of closed Schubert cells. Another consequence is a simple combinatorial interpretation of the chromatic polynomial of the inversion graph of a permutation which avoids the above patterns.
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