Results 71 to 80 of about 6,580 (165)
The scaling limit of random cubic planar graphs
Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.Abstract We study the random cubic planar graph Cn$\mathsf {C}_n$ with an even number n$n$ of vertices. We show that the Brownian map arises as Gromov–Hausdorff–Prokhorov scaling limit of Cn$\mathsf {C}_n$ as n∈2N$n \in 2 \mathbb {N}$ tends to infinity, after rescaling distances by γn−1/4$\gamma n^{-1/4}$ for a specific constant γ>0$\gamma >0$. This is
Benedikt Stufler
wiley +1 more source
Computing the Tutte Polynomial of a Matroid from its Lattice of Cyclic Flats [PDF]
, 2014 We show how the Tutte polynomial of a matroid $M$ can be computed from its condensed configuration, which is a statistic of its lattice of cyclic flats.
Eberhardt, Jens Niklas
core +1 more source
Valuative invariants for large classes of matroids
Journal of the London Mathematical Society, Volume 110, Issue 3, September 2024.Abstract We study an operation in matroid theory that allows one to transition a given matroid into another with more bases via relaxing a stressed subset. This framework provides a new combinatorial characterization of the class of (elementary) split matroids.
Luis Ferroni, Benjamin Schröter
wiley +1 more source
Orienting Transversals and Transition Polynomials of Multimatroids
, 2017 Multimatroids generalize matroids, delta-matroids, and isotropic systems, and transition polynomials of multimatroids subsume various polynomials for these latter combinatorial structures, such as the interlace polynomial and the Tutte-Martin polynomial.
Brijder, Robert
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Interlace polynomials and Tutte polynomials
, 2013 This article has been superseded by arXiv:1301 ...
openaire +2 more sources
Tutte polynomials and G-parking functions
Advances in Applied Mathematics, 2010 Let $G$ be a connected graph with vertex set $\{0,1,2,...,n\}$. We allow $G$ to have multiple edges and loops. In this paper, we give a characterization of external activity by some parameters of $G$-parking functions. In particular, we give the definition of the bridge vertex of a $G$-parking function and obtain an expression of the Tutte polynomial ...
Chang, Hungyung, Ma, Jun, Yeh, Yeong-Nan
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Mesh Parameterization Meets Intrinsic Triangulations
Computer Graphics Forum, Volume 43, Issue 5, August 2024.Abstract A parameterization of a triangle mesh is a realization in the plane so that all triangles have positive signed area. Triangle mesh parameterizations are commonly computed by minimizing a distortion energy, measuring the distortions of the triangles as they are mapped into the parameter domain.
Koray Akalin +3 more
wiley +1 more source
The Tutte Polynomial of a Morphism of Matroids 5. Derivatives as Generating Functions of Tutte Activities [PDF]
, 2012 We show that in an ordered matroid the partial derivative \partial^{p+q}t/\partialx^p\partialyq of the Tutte polynomial is p!q! times the generating function of activities of subsets with corank p and nullity q.
Vergnas, Michel Las
core
Zeros of Jones Polynomials for Families of Knots and Links
, 2001 We calculate Jones polynomials $V_L(t)$ for several families of alternating knots and links by computing the Tutte polynomials $T(G,x,y)$ for the associated graphs $G$ and then obtaining $V_L(t)$ as a special case of the Tutte polynomial.
Abe +65 more
core +3 more sources
European Journal of CombinatoricsThe classical Tutte polynomial is a two-variate polynomial $T_G(x,y)$ associated to graphs or more generally, matroids. In this paper, we introduce a polynomial $\widetilde{T}_H(x,y)$ associated to a bipartite graph $H$ that we call the permutation Tutte polynomial of the graph $H$.
Beke, Csongor +3 more
openaire +3 more sources