Results 81 to 90 of about 3,648 (134)

The Tutte q-Polynomial

, 2017
$q$-Matroids are defined on complemented modular support lattices. Minors of length 2 are of four types as in a "classical" matroid. Tutte polynomials $ (x,y)$ of matroids are calculated either by recursion over deletion/contraction of single elements, by an enumeration of bases with respect to internal/external activities, or by substitution $x \to ...
Bollen, Guus, Crapo, Henry, Jurrius, Relinde   +2 more
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Matroid connectivity and singularities of configuration hypersurfaces. [PDF]

Lett Math Phys, 2021
Denham G, Schulze M, Walther U.
europepmc   +1 more source

Ising Model on Random Triangulations of the Disk: Phase Transition. [PDF]

Commun Math Phys, 2023
Chen L, Turunen J.
europepmc   +1 more source

Generalized activities and the tutte polynomial

Discrete Mathematics, 1990
This paper examines the Tutte polynomial of a matroid (a generalization of the Tutte's polynomial of graph) from the point of view of basis activities. If \(r(S)\) is the rank of a subset \(S\) of the underlying set \(E\) in a matroid \(M\), then the Tutte polynomial \(t(M;x,y)\) of \(M\) is given by \[ t(M;x,y)=\sum_{S\subseteq E}(x-1)^{r(E)-r(S)}(y ...
Gordon, Gary, Traldi, Lorenzo
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An Interpretation for the Tutte Polynomial

European Journal of Combinatorics, 1999
For a matroid \(M\) which is representable over the rational numbers the author gives a new interpretation of the Tutte polynomial \(T_M(x,y)\) associated to \(M\). The Tutte polynomial \(T_M(x,y)\) of a matroid \(M\) is a or may be the fundamental invariant of \(M\). After its definition by \textit{W. T. Tutte} in 1947 [Proc. Camb. Philos. Soc. 43, 26-
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Weak maps and the Tutte polynomial

Advances in Applied Mathematics
Let $M$ 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.
Cho, Christine, Oxley, James
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Tutte polynomials in superspace

We associate a quotient of superspace to any hyperplane arrangement by considering the differential closure of an ideal generated by powers of certain homogeneous linear forms. This quotient is a superspace analogue of the external zonotopal algebra, and it further contains the central zonotopal algebra in the appropriate grading.
Rhoades, Brendon, Tewari, Vasu, Wilson, Andy   +2 more
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A Coarse Tutte Polynomial for Hypermaps

We give an analogue of the Tutte polynomial for hypermaps. This polynomial can be defined as either a sum over subhypermaps, or recursively through deletion-contraction reductions where the terminal forms consist of isolated vertices. Our Tutte polynomial extends the classical Tutte polynomial of a graph as well as the Tutte polynomial of an embedded ...
Ellis-Monaghan, Joanna A., Moffatt, Iain, Noble, Steven   +2 more
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Poisson traces, D-modules, and symplectic resolutions. [PDF]

Lett Math Phys, 2018
Etingof P, Schedler T.
europepmc   +1 more source

Dirac traces and the Tutte polynomial

Journal of High Energy Physics
Abstract Perturbative calculations involving fermion loops in quantum field theories require tracing over Dirac matrices. A simple way to regulate the divergences that generically appear in these calculations is dimensional regularisation, which has the consequence of replacing 4-dimensional Dirac matrices with d-dimensional ...
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