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| 2. |
- Eriksson, Henrik, et al.
(författare)
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Conjugacy of Coxeter elements
- 2009
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Ingår i: The Electronic Journal of Combinatorics. - 1097-1440 .- 1077-8926. ; 16:2, s. R4-
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Tidskriftsartikel (refereegranskat)
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| 3. |
- Eriksson, Kimmo, 1967-, et al.
(författare)
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The Chicken Braess Paradox
- 2019
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Ingår i: Mathematics Magazine. - : Taylor and Francis Inc.. - 0025-570X .- 1930-0980. ; 92:3, s. 213-221
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Tidskriftsartikel (refereegranskat)abstract
- Summary.: The Braess Paradox is the counterintuitive fact that creation of a shortcut may make travel slower. As each driver seeks to minimize his/her travel time, the shortcut may become so popular that it causes congestion elsewhere in the road network, thereby increasing the travel time for everyone. We extend the paradox by considering a shortcut that is a single-lane but two-way street. The conflict about which drivers get to use the single-lane shortcut is an example of a game theoretic situation known as Chicken, which merges with the Braess Paradox into the novel Chicken Braess Paradox: meeting traffic may make travel quicker.
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| 5. |
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| 6. |
- Eriksson, Henrik, et al.
(författare)
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Exact expectations for random graphs and assignments
- 2003
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Ingår i: Combinatorics, probability & computing. - 0963-5483 .- 1469-2163. ; 12, s. 401-412
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Tidskriftsartikel (refereegranskat)abstract
- For a random graph on n vertices where the edges appear with individual rates, we give exact formulas for the expected time at which the number of components has gone down to k and the expected length of the corresponding minimal spanning forest.For a random bipartite graph we give a formula for the expected time at which a k-assignment appears. This result has a bearing on the random assignment problem.
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| 7. |
- Eriksson, Henrik, et al.
(författare)
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Expected inversion number after k adjacent transpositions
- 2000
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Ingår i: Formal Power Series and Algebraic Combinatorics. - 3540672478 ; , s. 677-685
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Konferensbidrag (refereegranskat)abstract
- We give expressions for the expected number of inversions after t random adjacent transpositions have been performed on the identity permutation in Sn+1 The problem is a simplification of a problem motivated by genome evolution. For a fixed t and for all n greater than or equal to t, the expected number of inversions after t random adjacent transpositions isE-nt = t - 2/n ((t)(2)) + Sigma(r=2)(t) (-1)(r)/n(r) [2(r)C(r)((t)(r+1)) + 4d(r) ((t)(r))]where d(2) = 0, d(3) = 1, d(4) = 9, d(5) = 69,... is a certain integer sequence. An important part of the our method is the use of a heat. conduction analogy of the random walks, which guarantees certain properties of the solution.
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| 8. |
- Eriksson, Henrik, et al.
(författare)
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Note on the lamp lighting problem
- 2001
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Ingår i: Advances in Applied Mathematics. - : Elsevier BV. - 0196-8858 .- 1090-2074. ; 27:03-feb, s. 357-366
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Tidskriftsartikel (refereegranskat)abstract
- We answer some questions concerning the so-called sigma -game of Sutner [Linear cellular automata and the Garden of Eden, Math. Intelligencer 11 (1989), 49-53]. It is played on a graph where each vertex has a lamp, the light of which is toggled by pressing any vertex with an edge directed to the lamp. For example, we show that every configuration of lamps can be lit if and only if the number of complete matchings in the graph is odd. In the special case of an orthogonal grid one gets a criterion for whether the number of monomer-dimer tilings of an m x n grid is odd or even.
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| 9. |
- Eriksson, Kimmo, 1967-, et al.
(författare)
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Limit shapes of stable and recurrent configurations of a generalized bulgarian solitaire
- 2020
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Ingår i: Online Journal of Analytic Combinatorics. - : Department of Computer Science. - 1931-3365. ; :15
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Tidskriftsartikel (refereegranskat)abstract
- Bulgarian solitaire is played on n cards divided into several piles; a move consists of picking one card from each pile to form a new pile. This can be seen as a process on the set of integer partitions of n: If sorted configurations are represented by Young diagrams, a move in the solitaire consists of picking all cards in the bottom layer of the diagram and inserting the picked cards as a new column. Here we consider a generalization, L-solitaire, wherein a fixed set of layers L (that includes the bottom layer) are picked to form a new column. L-solitaire has the property that if a stable configuration of n cards exists it is unique. Moreover, the Young diagram of a configuration is convex if and only if it is a stable (fixpoint) configuration of some L-solitaire. If the Young diagrams representing card configurations are scaled down to have unit area, the stable configurations corresponding to an infinite sequence of pick-layer sets (L1, L2, . . .) may tend to a limit shape φ. We show that every convex φ with certain properties can arise as the limit shape of some sequence of Ln. We conjecture that recurrent configurations have the same limit shapes as stable configurations. For the special case Ln = {1, 1 + ⌊1/qn⌋, 1 + ⌊2/qn⌋, . . . }, where the pick layers are approximately equidistant with average distance 1/qn for some qn ∈ (0, 1], these limit shapes are linear (in case nq2n → 0), exponential (in case nq2n → ∞), or interpolating between these shapes (in case nq2n → C > 0).
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