| 1. |
- Aas, Erik, et al.
(författare)
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Limiting directions for random walks in classical affine Weyl groups
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Let be a finite Weyl group and the corresponding affine Weyl group. A random element of can be obtained as a reduced random walk on the alcoves of . By a theorem of Lam (Ann. Probab. 2015), such a walk almost surely approaches one of many directions. We compute these directions when is , and and the random walk is weighted by Kac and dual Kac labels. This settles Lam's questions for types and in the affirmative and for type in the negative. The main tool is a combinatorial two row model for a totally asymmetric simple exclusion process called the -TASEP, with four parameters. By specializing the parameters in different ways, we obtain TASEPs for each of the Weyl groups mentioned above. Computing certain correlations in these TASEPs gives the desired limiting directions.
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| 2. |
- Thörnblad, Karin, 1971, et al.
(författare)
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Scheduling optimization of a real flexible job shop including side constraints regarding maintenance, fixtures, and night shifts
- 2013
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We present a generic iterative scheduling procedure for the scheduling of a real flexible job shop, the so-called multitask cell at GKN Aerospace Engine Systems in Sweden. A time-indexed formulation of the problem is presented including side constraints regarding preventive maintenance, fixture availability, and unmanned night shifts. This paper continues the work in [35], with an improvement of the iterative solution procedure and the inclusion of constraints regarding night shifts during which only unmanned processing is allowed. The resulting schedules are compared with schedules constructed using two priority dispatching rules. Computational results show that the gain of including the night shifts constraints is significant and that the methodology developed is able to produce near-optimal schedules for industrial data instances for the coming shift within an acceptable practical time frame.
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| 3. |
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| 4. |
- Lundman, Anders, 1985-, et al.
(författare)
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A note on higher order Gauss Maps
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We study Gauss maps of order k, associated to a projective variety X embedded in projective space via a line bundle L. We show that if X is a smooth, complete complex variety and L is a k-jet spanned line bundle on X, with k > 1, then the Gauss map of order k has finite fibers, unless X = P^n is embedded by the Veronese embedding of order k. In the case where X is a toric variety, we give a combinatorial description of the Gauss maps of order k, its image and the general fibers.
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| 5. |
- Lundman, Anders, 1985-
(författare)
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Computing Seshardi constants on smooth toric surfaces
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we compute the Seshadri constants at the general point on many smooth polarized toric surfaces. We consider the case when the degree of jet separation is small or the core of the associated polygon is a line segment. Our main result is that in this case the Seshadri constant at the general point can often be determined in terms of easily computable invariants of the surfaces at hand. Lastly we consider the case that the core of the associated polygon is a point for a smooth polarized toric surface (X, L ). We show that in this case X can be constructed via consecutive equivariant blow-ups of either P^2 or P^1 x P^1.
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| 6. |
- Brändén, Petter, 1976
(författare)
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Counterexamples to the Neggers-Stanley conjecture
- 2004
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Ingår i: Electronic Research Announcements of the American Mathematical Society. - 1079-6762. ; 10, s. 155-158
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Annan publikation (övrigt vetenskapligt/konstnärligt)
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| 7. |
- Zhelezov, Dmitrii, 1987
(författare)
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Discrete spheres and arithmetic progressions in product sets
- 2015
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We prove that if B is a set of N positive integers such that B⋅B contains an arithmetic progression of length M then N≥π(M)+M2/3−o(1). On the other hand, there are examples for which N<π(M)+M2/3. This improves previously known bounds of the form N=Ω(π(M)) and N=O(π(M)), respectively. The main new tool is a reduction of the original problem to the question of an approximate additive decomposition of the 3-sphere in ?n3 which is the set of 0-1 vectors with exactly three non-zero coordinates. Namely, we prove that such a set cannot be contained in a sumset A+A unless |A|≫n2.
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| 8. |
- Alexandersson, Per, et al.
(författare)
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Refined Catalan and Narayana cyclic sieving
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We prove several new instances of the cyclic sieving phenomenon (CSP) on Catalan objects of type A and type B. Moreover, we refine many of the known instances of the CSP on Catalan objects. For example, we consider triangulations refined by the number of “ears”, non-crossing matchings with a fixed number of short edges, and non-crossing configurations with a fixed number of loops and edges.
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| 9. |
- Linusson, Svante, et al.
(författare)
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On random shifted standard Young tableaux and 132-avoiding sorting networks
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We study shifted standard Young tableaux (SYT). The limiting surface of uniformly random shifted SYT of staircase shape is determined, with the integers in the SYT as heights. This implies via properties of the Edelman-Greene bijection results about random 132-avoiding sorting networks, including limit shapes for trajectories and intermediate permutations. Moreover, the expected number of adjacencies in SYT is considered. It is shown that on average each row and each column of a shifted SYT of staircase shape contains precisely one adjacency.
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| 10. |
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