| 1. |
- Alexandersson, Per, et al.
(författare)
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Cyclic sieving, skew Macdonald polynomials and Schur positivity
- 2020
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Ingår i: Algebraic Combinatorics. - : Centre Mersenne. - 2589-5486. ; 3:4, s. 913-939
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Tidskriftsartikel (refereegranskat)abstract
- When λ is a partition, the specialized non-symmetric Macdonald polynomial Eλ(x; q; 0) is symmetric and related to a modified Hall–Littlewood polynomial. We show that whenever all parts of the integer partition λ are multiples of n, the underlying set of fillings exhibit the cyclic sieving phenomenon (CSP) under an n-fold cyclic shift of the columns. The corresponding CSP polynomial is given by Eλ(x; q; 0). In addition, we prove a refined cyclic sieving phenomenon where the content of the fillings is fixed. This refinement is closely related to an earlier result by B. Rhoades. We also introduce a skew version of Eλ(x; q; 0). We show that these are symmetric and Schur positive via a variant of the Robinson–Schenstedt–Knuth correspondence and we also describe crystal raising and lowering operators for the underlying fillings. Moreover, we show that the skew specialized non-symmetric Macdonald polynomials are in some cases vertical-strip LLT polynomials. As a consequence, we get a combinatorial Schur expansion of a new family of LLT polynomials.
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| 2. |
- 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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| 3. |
- Alexandersson, Per, et al.
(författare)
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Refined Catalan and Narayana cyclic sieving
- 2021
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Ingår i: Combinatorial Theory. - : California Digital Library (CDL). - 2766-1334. ; 1:0
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Tidskriftsartikel (refereegranskat)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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| 4. |
- Alexandersson, Per, et al.
(författare)
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Skew characters and cyclic sieving
- 2021
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Ingår i: Forum of Mathematics, Sigma. - : Cambridge University Press (CUP). - 2050-5094. ; 9, s. 1-31
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Tidskriftsartikel (refereegranskat)abstract
- In 2010, Rhoades proved that promotion on rectangular standard Young tableaux, together with the associated fake-degree polynomial, provides an instance of the cyclic sieving phenomenon. We extend this result to m-tuples of skew standard Young tableaux of the same shape, for fixed m, subject to the condition that the mth power of the associated fake-degree polynomial evaluates to nonnegative integers at roots of unity. However, we are unable to specify an explicit group action. Put differently, we determine in which cases the mth tensor power of a skew character of the symmetric group carries a permutation representation of the cyclic group.To do so, we use a method proposed by Amini and the first author, which amounts to establishing a bound on the number of border-strip tableaux of skew shape. Finally, we apply our results to the invariant theory of tensor powers of the adjoint representation of the general linear group. In particular, we prove the existence of a bijection between permutations and Stembridge’s alternating tableaux, which intertwines rotation and promotion.
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| 5. |
- Ekman, Joakim, 1970-, et al.
(författare)
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Demokratiseringsprocesser : Nya perspektiv och utmaningar
- 2023. - 3
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Bok (refereegranskat)abstract
- Varför utvecklas vissa länder men inte andra till väl fungerande demokratier? Är det ekonomisk utveckling, en viss uppsättning institutioner, en gynnsam medborgarkultur, civilsamhället, stödjande internationella förutsättningar eller samarbetande politiska eliter som avgör? Kan alla länder i världen bli demokratier, eller är vissa stater dömda att för alltid styras av auktoritära regimer?I denna uppdaterade tredje upplaga av Demokratiseringsprocesserpresenteras och granskas de viktigaste teoretiska och empiriska bidragen inom forskningen om demokratiseringsprocesser. Författarna introducerar centrala begrepp som demokrati, modernisering, transition, konsolidering och diffusion, samt visar hur forskningen har utvecklats från den tidiga efterkrigstiden fram till idag. Även demokratins tillbakagång och olika varianter av samtida auktoritära styrelseskick diskuteras. Boken inleds med ett förord av professor Li Bennich-Björkman.Demokratiseringsprocesser är särskilt lämplig för kurser i statsvetenskap, sociologi, internationella relationer, utvecklingsstudier, Europastudier samt freds- och konfliktforskning.
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| 6. |
- Mikaelsson, Rickard, 1975-
(författare)
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Promoting Democracy : Sweden and the democratisation process in Macedonia
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This dissertation contributes to an increased understanding of democracy promotion. Empirically, the study focuses on the multi-faced democratisation process in Macedonia; the official Swedish policy for democracy promotion; and actual Swedish attempts to promote democracy in Macedonia in the period 2000–2006. Theoretically, the study advances an analytical framework, which serves to bring clarity to democracy promotion as a concept. It is argued that democracy promotion embodies six structural components, and should be understood as activities adopted and/or supported by foreign actors, as part of a relationship between the democracy promoter and the recipient country, based on a set of motives and shaped through the use of different strategies, methods and channels. Moreover, the issue of impact is investigated. The analytical framework is used to investigate the character of Swedish democracy promotion, and to develop a typology of the roles of democracy promotion in democratisation processes. It is argued that the Swedish policy for democracy promotion is permeated by a Swedish democratic self-image, eclectic theoretical reflection, and flexibility. In addition, it is argued that Sweden is primarily driven by altruistic and ideological motives, and acts to promote legal and societal democracy, and that the allocation of democracy promotion resources is based on theoretical as well as practical considerations. Macedonia’s democratisation process is analysed, and on the basis of the Swedish attempts to promote democracy in Macedonia, the study advances a typology of the roles of democracy promotion in democratisation processes, these being: educator, initiator, and supporter. Together with the analytical framework, this role typology provides new possibilities to study, and understand, democracy promotion.
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