| 1. |
- 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
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Tidskriftsartikel (refereegranskat)abstract
- For a Coxeter group (W, S), a permutation of the set S is called a Coxeter word and the group element represented by the product is called a Coxeter element. Moving the first letter to the end of the word is called a rotation and two Coxeter elements are rotation equivalent if their words can be transformed into each other through a sequence of rotations and legal commutations. We prove that Coxeter elements are conjugate if and only if they are rotation equivalent. This was known for some special cases but not for Coxeter groups in general.
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| 2. |
- Eriksson, Henrik, et al.
(författare)
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Dense packing of patterns in a permutation
- 2007
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Ingår i: Annals of Combinatorics. - : Springer Science and Business Media LLC. - 0218-0006 .- 0219-3094. ; 11:3-4, s. 459-470
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Tidskriftsartikel (refereegranskat)abstract
- We study the length L-k of the shortest permutation containing all patterns of length k. We establish the bounds e(-2)k(2) < L-k <= (2/3 + o(1))k(2). We also prove that as k there are permutations of length (1/4+o(1))k(2) containing almost all patterns of length k.
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| 3. |
- 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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| 4. |
- Eriksson, Henrik, et al.
(författare)
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Sorting a bridge hand
- 2001
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Ingår i: Discrete Mathematics. - 0012-365X .- 1872-681X. ; 241:1-3, s. 289-300
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Tidskriftsartikel (refereegranskat)abstract
- Sorting a permutation by block moves is a task that every bridge player has to solve every time she picks up a new hand of cards. It is also a problem for the computational biologist, for block moves are a fundamental type of mutation that can explain why genes common to two species do not occur in the same order in the chromosome, It is not known whether there exists an optimal sorting procedure running in polynomial time. Bafna and Pevzner gave a polynomial time algorithm that sorts any permutation of length n in at most 3n/4 moves. Our new algorithm improves this to [(2n - 2)/3] for n greater than or equal to 9. For the reverse permutation, we give an exact expression for the number of moves needed, namely [(n + 1)/2]. Computations of Bafha and Pevzner up to n = 10 seemed to suggest that this is the worst case; but as it turns out, a first counterexample occurs for n = 13, i.e. the bridge player's case. Professional card players never sort by rank, only by suit. For this case, we give a complete answer to the optimal sorting problem.
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| 5. |
- 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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| 6. |
- Engström, Emma, PhD, 1982-, et al.
(författare)
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Global variations in online privacy concerns across 57 countries
- 2023
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Ingår i: Computers in Human Behavior Reports. - : Elsevier B.V.. - 2451-9588 .- 0747-5632 .- 1873-7692. ; 9
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Tidskriftsartikel (refereegranskat)abstract
- Cross-cultural studies have found national differences in how concerned people are about online privacy. However, it has not yet been settled what causes this variation, and several factors have been proposed in the literature, including internet habituation, individualism, and uncertainty avoidance. Here we investigate these factors by two studies. In the first, we examine the association between online privacy concerns and a new measure of online self-disclosure norms that we introduce. We find that this measure is significantly associated with two established instruments of online privacy concerns in the literature. In the second, we analyze previously unpublished data from a questionnaire on online self-disclosure norms as assessed by this new measure. It includes replies from 18,046 adult respondents from 57 countries and six continents. We find that norms in favor of more restrictive online self-disclosure are weaker in countries with higher levels of internet penetration (r = −0.56, p < .001). Our findings suggest that higher internet penetration in a country reduces online privacy concerns. The results support the idea that habituation to online environments decreases privacy risk perceptions. An implication is that preferences for online privacy are likely to decline over time in countries where internet penetration is still low. Lastly, in conflict with previous studies, our analyses do not support the theory that online privacy concerns are associated with national cultures related to individualism or uncertainty avoidance as measured by Hofstede's indices.
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| 7. |
- Enquist, Magnus, et al.
(författare)
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One cultural parent makes no culture
- 2010
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Ingår i: Animal Behaviour. - : Elsevier BV. - 0003-3472 .- 1095-8282. ; 79:6, s. 1353-1362
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Tidskriftsartikel (refereegranskat)abstract
- The ability to acquire knowledge and skills from others is widespread in animals and is commonly thought to be responsible for the behavioural traditions observed in many species. However, in spite of the extensive literature on theoretical analyses and empirical studies of social learning, little attention has been given to whether individuals acquire knowledge from a single individual or multiple models. Researchers commonly refer to instances of sons learning from fathers, or daughters from mothers, while theoreticians have constructed models of uniparental transmission, with little consideration of whether such restricted modes of transmission are actually feasible. We used mathematical models to demonstrate that the conditions under which learning from a single cultural parent can lead to stable culture are surprisingly restricted ( the same reasoning applies to a single social-learning event). Conversely, we demonstrate how learning from more than one cultural parent can establish culture, and find that cultural traits will reach a nonzero equilibrium in the population provided the product of the fidelity of social learning and the number of cultural parents exceeds 1. We discuss the implications of the analysis for interpreting various findings in the animal social-learning literature, as well as the unique features of human culture.
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| 8. |
- Eriksson, Kimmo, et al.
(författare)
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Asymmetric equilibria in dynamic two-sided matching markets with independent preferences
- 2008
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Ingår i: International Journal of Game Theory. - : Springer Science and Business Media LLC. - 0020-7276 .- 1432-1270. ; 36, s. 421-440
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Tidskriftsartikel (refereegranskat)abstract
- A fundamental fact in two-sided matching is that if amarket allows several stable outcomes, then one is optimal for all men in the sense that no man would prefer another stable outcome.We study a related phenomenon of asymmetric equilibria in a dynamic market where agents enter and search for a mate for at most n rounds before exiting again. Assuming independent preferences, we find that this game has multiple equilibria, some of which are highly asymmetric between sexes. We also investigate how the set of equilibria depends on a sex difference in the outside option of not being mated at all.
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| 9. |
- Eriksson, Kimmo, et al.
(författare)
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Bentley’s conjecture on popularity toplist turnover under random copying
- 2010
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Ingår i: The Ramanujan journal. - : Springer Science and Business Media LLC. - 1382-4090 .- 1572-9303. ; 23, s. 371-396
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Tidskriftsartikel (refereegranskat)abstract
- Bentley et al studied the turnover rate in popularity toplists in a ’random copying’ model of cultural evolution. Based on simulations of a model with population size N, list length ℓ and invention rate μ, they conjectured a remarkably simple formula for the turnover rate: ℓ√μ. Here we study an overlapping generations version of the random copying model, which can be interpreted as a random walk on the integer partitions of the population size. In this model we show that the conjectured formula, after a slight correction, holds asymptotically.
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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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