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- Andrén, Lina J., 1980-
(författare)
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On Latin squares and avoidable arrays
- 2010
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of the four papers listed below and a survey of the research area. I Lina J. Andrén: Avoiding (m, m, m)-arrays of order n = 2k II Lina J. Andrén: Avoidability of random arrays III Lina J. Andr´en: Avoidability by Latin squares of arrays with even order IV Lina J. Andrén, Carl Johan Casselgren and Lars-Daniel Öhman: Avoiding arrays of odd order by Latin squares Papers I, III and IV are all concerned with a conjecture by Häggkvist saying that there is a constant c such that for any positive integer n, if m ≤ cn, then for every n × n array A of subsets of {1, . . . , n} such that no cell contains a set of size greater than m, and none of the elements 1, . . . , n belongs to more than m of the sets in any row or any column of A, there is a Latin square L on the symbols 1, . . . , n such that there is no cell in L that contains a symbol that belongs to the set in the corresponding cell of A. Such a Latin square is said to avoid A. In Paper I, the conjecture is proved in the special case of order n = 2k . Paper III improves on the techniques of Paper I, expanding the proof to cover all arrays of even order. Finally, in Paper IV, similar methods are used together with a recoloring theorem to prove the conjecture for all orders. Paper II considers another aspect of the problem by asking to what extent way a deterministic result concerning the existence of Latin squares that avoid certain arrays can be used when the sets in the array are assigned randomly.
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- Eriksson, Henrik, et al.
(författare)
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Words with intervening neighbours in infinite Coxeter groups are reduced
- 2010
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Ingår i: The Electronic Journal of Combinatorics. - : The Electronic Journal of Combinatorics. - 1097-1440 .- 1077-8926. ; 17:1, s. N9-
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Tidskriftsartikel (refereegranskat)abstract
- Consider a graph with vertex set S. A word in the alphabet S has the intervening neighbours property if any two occurrences of the same letter are separated by all its graph neighbours. For a Coxeter graph, words represent group elements. Speyer recently proved that words with the intervening neighbours property are reduced if the group is infinite and irreducible. We present a new and shorter proof using the root automaton for recognition of reduced words.
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| 4. |
- 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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| 5. |
- 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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| 6. |
- Jonsson, Markus, et al.
(författare)
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Markov chains on graded posets : Compatibility of up-directed and down-directed transition probabilities
- 2018
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Ingår i: Order. - : Springer Netherlands. - 0167-8094 .- 1572-9273. ; :1, s. 93-109
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Tidskriftsartikel (refereegranskat)abstract
- We consider two types of discrete-time Markov chains where thestate space is a graded poset and the transitionsare taken along the covering relations in the poset. The first type of Markov chain goes only in one direction, either up or down in the poset (an up chain or down chain). The second type toggles between two adjacent rank levels (an up-and-down chain). We introduce two compatibility concepts between the up-directed transition probabilities (an up rule) and the down-directed(a down rule), and we relate these to compatibility betweenup-and-down chains. This framework is used to prove a conjecture about a limit shape for a process on Young's lattice. Finally, we settle the questions whether the reverse of an up chain is a down chain for some down rule and whether there exists an up or down chain at all if the rank function is not bounded.
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| 9. |
- Stenberg, Fredrik, 1975-
(författare)
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Semi-Markov Models for Insurance and Option Rewards
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis presents studies of semi-Markov models for insurance and option rewards. The thesis consists of the introduction and six papers. The introduction presents the results of the thesis in an informal way.In paper A, a general semi-Markov reward model is presented. Recurrence relations for evaluation of higher moments of the reward process are given, as well as a backward semi-Markov reward processes are applied to insurance problems for the first time.In paper B, models for disability insurance given in paper A are further extended. Statistical evidences of relevance of semi-Markov setting are given. Applications to profit-risk analysis for contracts are considered.In paper C, a more detailed explanation of the algorithmic for the non-homogenous backward semi-Markov reward process is given. Two algorithmic approaches to solve the problem in an iterative manner are given. One of the algorithms is presented in a pseudo-code.In paper D, the geometrical Brownian motion with drift and volatility controlled by a semi-Markov processes is considered as a price process in option valuation. The discrete version is examined and limit theorems describing the transition from discrete to continuous time are given. Monte-Carlo algorithms are described.In paper E, a general price process represented by a two-component Markov process is considered. American options with pay-off functions, which admit power type upper bounds are studied. Both the transition characteristics of the price processes and the pay-off functions are assumed to depend on a perturbation parameter and to converge to the corresponding limits. Results about the convergence of reward functionals for American options are presented.In paper F, convergence for option rewards when the price processes are perturbed exponential Lévy type process controlled by semi-Markov indices is studied. Both European and American type options with pay-off functions which admit power type upper bounds are considered. The paper continues research started in paper D and gives a key example for paper E.
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| 10. |
- Eriksson, Kimmo, et al.
(författare)
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Limiting shapes of birth-and-death processes on Young diagrams
- 2012
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Ingår i: Advances in Applied Mathematics. - : Elsevier BV. - 0196-8858 .- 1090-2074. ; 48:4, s. 575-602
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Tidskriftsartikel (refereegranskat)abstract
- We consider a family of birth processes and birth-and-death processes on Young diagrams of integer partitions of n. This family incorporates three famous models from very different fields: Rost's totally asymmetric particle model (in discrete time), Simon's urban growth model, and Moran's infinite alleles model. We study stationary distributions and limit shapes as n tends to infinity, and present a number of results and conjectures.
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