Relevant bibliographies by topics / Polytope des couplages parfaits

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  2. Dissertations / Theses

Academic literature on the topic 'Polytope des couplages parfaits'

Author: Grafiati
Published: 7 July 2024
Last updated: 31 July 2025

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Journal articles on the topic "Polytope des couplages parfaits"

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Kim, Jang Soo. "Proofs of two conjectures of Kenyon and Wilson on Dyck tilings." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AR,..., Proceedings (2012). http://dx.doi.org/10.46298/dmtcs.3046.

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International audience Recently, Kenyon and Wilson introduced a certain matrix M in order to compute pairing probabilities of what they call the double-dimer model. They showed that the absolute value of each entry of the inverse matrix $M^-1$ is equal to the number of certain Dyck tilings of a skew shape. They conjectured two formulas on the sum of the absolute values of the entries in a row or a column of $M^-1$. In this paper we prove the two conjectures. As a consequence we obtain that the sum of the absolute values of all entries of $M^-1$ is equal to the number of complete matchings. We
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Musiker, Gregg, and Ralf Schiffler. "Cluster algebras of unpunctured surfaces and snake graphs." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AK,..., Proceedings (2009). http://dx.doi.org/10.46298/dmtcs.2685.

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International audience We study cluster algebras with principal coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of perfect matchings of a certain graph $G_{T,\gamma}$ that is constructed from the surface by recursive glueing of elementary pieces that we call tiles. We also give a second formula for these Laurent polynomial expansions in terms of subgraphs of the graph $G_{T,\gamma}$ . Nous étudions des algèbres amassées avec coefficients principaux associées au
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3

Rubey, Martin, and Bruce W. Westbury. "Combinatorics of symplectic invariant tensors." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings, 27th..., Proceedings (2015). http://dx.doi.org/10.46298/dmtcs.2508.

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International audience An important problem from invariant theory is to describe the subspace of a tensor power of a representation invariant under the action of the group. According to Weyl's classic, the first main (later: 'fundamental') theorem of invariant theory states that all invariants are expressible in terms of a finite number among them, whereas a second main theorem determines the relations between those basic invariants.Here we present a transparent, combinatorial proof of a second fundamental theorem for the defining representation of the symplectic group $Sp(2n)$. Our formulatio
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Heitsch, Christine E., and Prasad Tetali. "Meander Graphs." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AO,..., Proceedings (2011). http://dx.doi.org/10.46298/dmtcs.2926.

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International audience We consider a Markov chain Monte Carlo approach to the uniform sampling of meanders. Combinatorially, a meander $M = [A:B]$ is formed by two noncrossing perfect matchings, above $A$ and below $B$ the same endpoints, which form a single closed loop. We prove that meanders are connected under appropriate pairs of balanced local moves, one operating on $A$ and the other on $B$. We also prove that the subset of meanders with a fixed $B$ is connected under a suitable local move operating on an appropriately defined meandric triple in $A$. We provide diameter bounds under such
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Dissertations / Theses on the topic "Polytope des couplages parfaits"

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Pisanu, Francesco. "On box-total dual integrality and total equimodularity." Electronic Thesis or Diss., Paris 13, 2023. http://www.theses.fr/2023PA131044.

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Dans cette thèse, nous étudions les polyèdres total dual box-intègraux (box-TDI) associés à plusieurs problèmes et matrices totalement équimodulaires. De plus, nous étudions la complexité de certaines questions fondamentales liées à ces polyèdres. Nous commençons par considérer les matrices totalement équimodulaires, qui sont des matrices telles que, pour chaque sous-ensemble de lignes linéairement indépendantes, toutes les sous-matrices maximales non-singulières ont le même déterminant en valeur absolue. Malgré leurs similitudes avec les matrices totalement unimodulaires, nous mettons en évid
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2

Dupont, Bouillard Alexandre. "Co-k-plexes and k-defective coloring : polytopes and algorithms." Electronic Thesis or Diss., Paris 13, 2024. http://www.theses.fr/2024PA131019.

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Cette thèse propose plusieurs résultats sur les co-k-plexes, qui sont des ensembles de sommets induisant un graphe avec un degré maximum k-1. La première partie de la thèse explore plusieurs caractérisations d'une nouvelle sous-classe de graphes parfaits, appelés graphes contraction parfaits. Ce sont l'ensemble des graphes parfaits restant parfaits après contraction de n'importe quel ensemble d'arêtes. Cette classe de graphes est caractérisée de quatre manières différentes. Parmi ces résultats, un graphe est contraction parfait si et seulement s'il est parfait et que la contraction de n'import
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3

Benchetrit, Yohann. "Propriétés géométriques du nombre chromatique : polyèdres, structures et algorithmes." Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAM049/document.

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Le calcul du nombre chromatique et la détermination d'une colo- ration optimale des sommets d'un graphe sont des problèmes NP- difficiles en général. Ils peuvent cependant être résolus en temps po- lynomial dans les graphes parfaits. Par ailleurs, la perfection d'un graphe peut être décidée efficacement. Les graphes parfaits sont caractérisés par la structure de leur poly- tope des stables : les facettes non-triviales sont définies exclusivement par des inégalités de cliques. Réciproquement, une structure similaire des facettes du polytope des stables détermine-t-elle des propriétés combinatoi
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