Results 71 to 80 of about 156 (150)
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
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Discrete Mathematics, 2001 The authors look at the Tutte polynomials of \(q\)-cones \((q\)-lifts) of combinatorial geometries (simple matroids) representable over \(\text{GF}(q)\). A formula is derived for the Tutte polynomial of all \(q\)-cones of \(G\) in terms of the Tutte polynomial of \(G\).
Joseph E. Bonin, Hongxun Qin
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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
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On coefficients of the Tutte polynomial
Discrete Mathematics, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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
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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 $H$.
Csongor Beke +3 more
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GEOMETRIC BIJECTIONS FOR REGULAR MATROIDS, ZONOTOPES, AND EHRHART THEORY
Forum of Mathematics, Sigma, 2019 Let $M$ be a regular matroid. The Jacobian group $\text{Jac}(M)$ of $M$ is a finite abelian group whose cardinality is equal to the number of bases of $M$.
SPENCER BACKMAN +2 more
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The Electronic Journal of CombinatoricsThe Tutte polynomial and Derksen's $\mathcal{G}$-invariant are the universal deletion-contraction and valuative matroid and polymatroid invariants, respectively. There are only a handful of well known invariants (like the matroid Kazhdan-Lusztig polynomials) between (in terms of fineness) the Tutte polynomial and Derksen's $\mathcal{G}$-invariant.
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Weak maps and the Tutte polynomial
Advances in Applied MathematicsLet $M$ and $N$ be matroids such that $N$ is the image of $M$ under a rank-preserving weak map. Generalizing results of Lucas, we prove that, for $x$ and $y$ positive, $T(M;x,y)\geq T(N;x,y)$ if and only if $x+y\geq xy$ or $M\cong N$. We give a number of consequences of this result.
Christine Cho, James G. Oxley
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Splitting Formulas for Tutte Polynomials
Journal of Combinatorial Theory, Series B, 1997 The Tutte polynomial is a central invariant of a matroid. In particular, many numerical invariants of a matroid can be calculated by evaluating or calculating coefficients of the Tutte polynomial. Moreover, for certain cases there is a close connection between the Tutte polynomial and the Jones and Kauffman polynomial of a link.
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