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Refined Counting of Fully Packed Loop Configurations
Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory. Linköping University, The Institute of Technology.
2007 (English)In: Séminaire Lotharingien de Combinatoire, ISSN 1286-4889, Vol. 56, 1-27 p.Article in journal (Refereed) Published
Abstract [en]

We give a generalisation of a conjecture by Propp on a summation formula for fully packed loop configurations. The original conjecture states that the number of configurations in which each external edge is connected to its neighbour is equal to the total number of configurations of size one less. This conjecture was later generalised by Zuber to include more types of configurations. Our conjecture further refines the counting and provides a general framework for some other summation formulas observed by Zuber. It also implies similar summation formulas for half-turn symmetric configurations.

Place, publisher, year, edition, pages
2007. Vol. 56, 1-27 p.
National Category
URN: urn:nbn:se:liu:diva-12703OAI: diva2:16886
Available from: 2007-10-29 Created: 2007-10-29
In thesis
1. Combinatorial Considerations on Two Models from Statistical Mechanics
Open this publication in new window or tab >>Combinatorial Considerations on Two Models from Statistical Mechanics
2007 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

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.

Place, publisher, year, edition, pages
Matematiska institutionen, 2007. 7 p.
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1335
fully packed loop model, rhombus tilings, hard particle model, independence complex, discrete morse theory
National Category
Discrete Mathematics
urn:nbn:se:liu:diva-10141 (URN)LIU-TEK-LIC-2007:44 (Local ID)978-91-85895-44-1 (ISBN)LIU-TEK-LIC-2007:44 (Archive number)LIU-TEK-LIC-2007:44 (OAI)
2007-11-16, 10:15 (English)
Available from: 2007-10-29 Created: 2007-10-29 Last updated: 2010-01-12

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Thapper, Johan
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TCSLAB - Theoretical Computer Science LaboratoryThe Institute of Technology

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