| 1. |
- Janson, Svante, 1955-, et al.
(författare)
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Proportionella val inom kommunfullmäktige
- 2019
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Vi diskuterar två olika problem som kan uppstå vid proportionella val i kommunfullmäktige och regionfullmäktige når ett parti försöker en kupp genom att utan samtycke gå i kartell med ett annat parti vid val till nämnd eller styrelse, vilket aktualiserades i åtminstone ett par fall hösten 2018. Det första problemet är vad sådana oönskade valkarteller kan få för effekter, och vilka möjligheter det finns för ett parti att skydda sig från att bli del i en oönskad valkartell. Det andra problemet är att i en sådan valkartell kan ett parti genom att splittra upp sina kandidater strategiskt på flera olika valsedlar få fler platser i en nämnd är vad som är proportionellt. Detta andra problem bottnar i att lagen om proportionella val stipulerar att Thieles metod skall användas för fördelning inom kartellen. På detta problem finns en enkel matematisk lösning och vi argumenterar för att man skall byta till Phragméns metod som används för motsvarande val till utskott i riksdagen.
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| 2. |
- Aas, Erik, et al.
(författare)
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Continuous multi-line queues and TASEP
- 2018
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Ingår i: ANNALES DE L INSTITUT HENRI POINCARE D. - : EUROPEAN MATHEMATICAL SOC. - 2308-5827. ; 5:1, s. 127-152
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study a distribution Xi of labeled particles on a continuous ring. It arises in three different ways, all related to the multi-type TASEP on a ring. We prove formulas for the probability density function for some permutations and give conjectures for a larger class. We give a complete conjecture for the probability of two particles i, j being next to each other on the cycle, for which we prove some cases. We also find that two natural events associated to the process have exactly the same probability expressed as a Vandermonde determinant. It is unclear whether this is just a coincidence or a consequence of a deeper connection.
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| 3. |
- Aas, E., et al.
(författare)
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The exact phase diagram for a semipermeable TASEP with nonlocal boundary jumps
- 2019
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Ingår i: Journal of Physics A. - : Institute of Physics Publishing (IOPP). - 1751-8113 .- 1751-8121. ; 52:35
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Tidskriftsartikel (refereegranskat)abstract
- We consider a finite one-dimensional totally asymmetric simple exclusion process with four types of particles, {1, 0, 1, }, in contact with reservoirs. Particles of species 0 can neither enter nor exit the lattice, and those of species are constrained to lie at the first and last site. Particles of species 1 enter from the left reservoir into either the first or second site, move rightwards, and leave from either the last or penultimate site. Conversely, particles of species 1 enter from the right reservoir into either the last or penultimate site, move leftwards, and leave from either the first or last site. This dynamics is motivated by a natural random walk on the Weyl group of type D. We compute the exact nonequilibrium steady state distribution using a matrix ansatz building on earlier work of Arita. We then give explicit formulas for the nonequilibrium partition function as well as densities and currents of all species in the steady state, and derive the phase diagram.
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| 4. |
- Alexandersson, Per, et al.
(författare)
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The cyclic sieving phenomenon on circular Dyck paths
- 2019
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Ingår i: The Electronic Journal of Combinatorics. - : ELECTRONIC JOURNAL OF COMBINATORICS. - 1097-1440 .- 1077-8926. ; 26:4
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Tidskriftsartikel (refereegranskat)abstract
- We give a q-enumeration of circular Dyck paths, which is a superset of the classical Dyck paths enumerated by the Catalan numbers. These objects have recently been studied by Alexandersson and Panova. Furthermore, we show that this q-analogue exhibits the cyclic sieving phenomenon under a natural action of the cyclic group. The enumeration and cyclic sieving is generalized to Mobius paths. We also discuss properties of a generalization of cyclic sieving, which we call subset cyclic sieving, and introduce the notion of Lyndon-like cyclic sieving that concerns special recursive properties of combinatorial objects exhibiting the cyclic sieving phenomenon.
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| 5. |
- Asinowski, A., et al.
(författare)
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Pop-stack sorting and its image : Permutations with overlapping runs
- 2019
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Ingår i: Acta Mathematica Universitatis Comenianae. - : Comenius University in Bratislava, Jessenius Faculty of Medicine in Martin, Slovakia. - 0862-9544 .- 0231-6986. ; 88:3, s. 395-402
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Tidskriftsartikel (refereegranskat)abstract
- Pop-stack sorting is an important variation for sorting permutations via a stack. A single iteration of pop-stack sorting is the transformation T : S-n -> S-n that reverses all the maximal descending sequences of letters in a permutation. We investigate structural and enumerative aspects of pop-stacked permutations - the permutations that belong to the image of S-n under T. This work is part of a project aiming to provide the full combinatorial analysis of sorting with a pop-stack, as it was successfully done for sorting with a stack (though, even in this case, some famous problems are still open). The first results already show that pop-stack sorting has a very rich combinatorial structure, and leads to surprising phenomena.
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| 6. |
- Ayyer, A., et al.
(författare)
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Bumping sequences and multispecies juggling
- 2018
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Ingår i: Advances in Applied Mathematics. - : Academic Press. - 0196-8858 .- 1090-2074. ; 98, s. 100-126
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Tidskriftsartikel (refereegranskat)abstract
- Building on previous work by four of us (ABCN), we consider further generalizations of Warrington's juggling Markov chains. We first introduce “multispecies” juggling, which consist in having balls of different weights: when a ball is thrown it can possibly bump into a lighter ball that is then sent to a higher position, where it can in turn bump an even lighter ball, etc. We both study the case where the number of balls of each species is conserved and the case where the juggler sends back a ball of the species of its choice. In this latter case, we actually discuss three models: add-drop, annihilation and overwriting. The first two are generalisations of models presented in (ABCN) while the third one is new and its Markov chain has the ultra fast convergence property. We finally consider the case of several jugglers exchanging balls. In all models, we give explicit product formulas for the stationary probability and closed form expressions for the normalisation factor if known.
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| 7. |
- Ayyer, Arvind, et al.
(författare)
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Correlations in the multispecies tasep and a conjecture by Lam
- 2017
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Ingår i: Transactions of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9947 .- 1088-6850. ; 369:2, s. 1097-1125
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Tidskriftsartikel (refereegranskat)abstract
- We study correlations in the multispecies TASEP on a ring. Results on the correlation of two adjacent points prove two conjectures by Thomas Lam on (a) the limiting direction of a reduced random walk in (A) over tilde (n-1) and (b) the asymptotic shape of a random integer partition with no hooks of length n, a so called n-core. We further investigate two-point correlations far apart and three-point nearest neighbour correlations and prove explicit formulas in almost all cases. These results can be seen as a finite strengthening of correlations in the TASEP speed process by Amir, Angel and Valko. We also give conjectures for certain higher order nearest neighbour correlations. We find an unexplained independence property (provably for two points, conjecturally for more points) between points that are closer in position than in value that deserves more study.
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| 8. |
- Ayyer, Arvind, et al.
(författare)
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Reverse juggling processes
- 2019
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Ingår i: Random structures & algorithms (Print). - : WILEY. - 1042-9832 .- 1098-2418. ; 55:1, s. 56-72
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Tidskriftsartikel (refereegranskat)abstract
- Knutson introduced two families of reverse juggling Markov chains (single and multispecies) motivated by the study of random semi-infinite matrices over Fq. We present natural generalizations of both chains by placing generic weights that still lead to simple combinatorial expressions for the stationary distribution. For permutations, this is a seemingly new multivariate generalization of the inversion polynomial.
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| 9. |
- Ayyer, Arvind, et al.
(författare)
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Some generalized juggling processes (extended abstract)
- 2015
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Ingår i: DMTCS proc. FPSAC'15. - Nancy, France. ; , s. 925-936
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Konferensbidrag (refereegranskat)abstract
- We consider generalizations of juggling Markov chains introduced by Ayyer, Bouttier, Corteel and Nunzi. We first study multispecies generalizations of all the finite models therein, namely the MJMC, the add-drop and the annihilation models. We then consider the case of several jugglers exchanging balls. In all cases, we give explicit product formulas for the stationary probability and closed-form expressions for the normalization factor if known.
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| 10. |
- Leander, Madeleine, et al.
(författare)
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Correlation of Paths Between Distinct Vertices in a Randomly Oriented Graph
- 2015
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Ingår i: Mathematica Scandinavica. - : Det Kgl. Bibliotek/Royal Danish Library. - 0025-5521 .- 1903-1807. ; 116:2, s. 287-300
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Tidskriftsartikel (refereegranskat)abstract
- We prove that in a random tournament the events {s -> a} (meaning that there is a directed path from s to a) and {t -> b} are positively correlated, for distinct vertices a, s, b,t is an element of K-n. It is also proven that the correlation between the events {s -> a} and {t -> b} in the random graphs G(n, p) and G(n, m) with random orientation is positive for every fixed p > 0 and sufficiently large n (with m = Is left perpendicularp((n)(2))left perpendicular). We conjecture it to be positive for all p and all n. An exact recursion for P({s -> a} boolean AND {t -> b} in G(n, p) is given.
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