| 1. |
- Eriksson, Henrik, et al.
(author)
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Exact expectations for random graphs and assignments
- 2003
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In: Combinatorics, probability & computing. - 0963-5483 .- 1469-2163. ; 12, s. 401-412
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Journal article (peer-reviewed)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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| 2. |
- Eriksson, Henrik, et al.
(author)
-
Expected inversion number after k adjacent transpositions
- 2000
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In: Formal Power Series and Algebraic Combinatorics. - 3540672478 ; , s. 677-685
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Conference paper (peer-reviewed)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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| 3. |
- Eriksson, Henrik, et al.
(author)
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Note on the lamp lighting problem
- 2001
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In: Advances in Applied Mathematics. - : Elsevier BV. - 0196-8858 .- 1090-2074. ; 27:03-feb, s. 357-366
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Journal article (peer-reviewed)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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