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Combinatorial Consi...
Combinatorial Considerations on Two Models from Statistical Mechanics
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- Thapper, Johan, 1977- (författare)
- Linköpings universitet,TCSLAB - Laboratoriet för teoretisk datalogi,Tekniska högskolan
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- Linusson, Svante (preses)
- Linköpings universitet,Tillämpad matematik,Tekniska högskolan
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- Jonsson, Peter (preses)
- Linköpings universitet,TCSLAB - Laboratoriet för teoretisk datalogi,Tekniska högskolan
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- Jonsson, Jakob, Dr. (opponent)
- Matematiska institutionen, Kungliga Tekniska H¨ogskolan, Stockholm
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(creator_code:org_t)
- ISBN 9789185895441
- Matematiska institutionen, 2007
- Engelska 7 s.
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Serie: Linköping Studies in Science and Technology. Thesis, 0280-7971 ; 1335
- Relaterad länk:
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https://liu.diva-por...
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https://liu.diva-por... (primary) (Raw object)
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Abstract
Ämnesord
Stäng
- Interactions between combinatorics and statistical mechanics have provided many fruitful insights in both fields. A compelling example is Kuperberg’s solution to the alternating sign matrix conjecture, and its following generalisations. In this thesis we investigate two models from statistical mechanics which have received attention in recent years.The first is the fully packed loop model. A conjecture from 2001 by Razumov and Stroganov opened the field for a large ongoing investigation of the O(1) loop model and its connections to a refinement of the fully packed loop model. We apply a combinatorial bijection originally found by de Gier to an older conjecture made by Propp.The second model is the hard particle model. Recent discoveries by Fendley et al. and results by Jonsson suggests that the hard square model with cylindrical boundary conditions possess some beautiful combinatorial properties. We apply both topological and purely combinatorial methods to related independence complexes to try and gain a better understanding of this model.
Ämnesord
- NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Discrete Mathematics (hsv//eng)
Nyckelord
- fully packed loop model
- rhombus tilings
- hard particle model
- independence complex
- discrete morse theory
- Discrete mathematics
- Diskret matematik
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