Results 31 to 40 of about 6,580 (165)
Graded Linearity of Stanley–Reisner Ring of Broken Circuit Complexes
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 This paper introduces two new notions of graded linear resolution and graded linear quotients, which generalize the concepts of linear resolution property and linear quotient for modules over the polynomial ring A = k[x1, …, xn]. Besides, we compare graded linearity with componentwise linearity in general.
Mohammad Reza-Rahmati +2 more
wiley +1 more source
K-classes for matroids and equivariant localization [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 To every matroid, we associate a class in the K-theory of the Grassmannian. We study this class using the method of equivariant localization. In particular, we provide a geometric interpretation of the Tutte polynomial.
Alex Fink, David Speyer
doaj +1 more source
Recipe theorem for the Tutte polynomial for matroids, renormalization group-like approach [PDF]
, 2013 Using a quantum field theory renormalization group-like differential equation, we give a new proof of the recipe theorem for the Tutte polynomial for matroids.
Duchamp, Gérard H. E. +3 more
core +3 more sources
Fourientations and the Tutte polynomial [PDF]
Research in the Mathematical Sciences, 2017 A fourientation of a graph is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it. Fixing a total order on the edges and a reference orientation of the graph, we investigate properties of cuts and cycles in fourientations which give trivariate generating functions that are generalized
Backman, Spencer, Hopkins, Sam
openaire +5 more sources
The Incidence Hopf Algebra of Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 The graph algebra is a commutative, cocommutative, graded, connected incidence Hopf algebra, whose basis elements correspond to finite simple graphs and whose Hopf product and coproduct admit simple combinatorial descriptions.
Brandon Humpert, Jeremy L. Martin
doaj +1 more source
Relative Tutte polynomials of tensor products of colored graphs [PDF]
, 2012 The tensor product $(G_1,G_2)$ of a graph $G_1$ and a pointed graph $G_2$ (containing one distinguished edge) is obtained by identifying each edge of $G_1$ with the distinguished edge of a separate copy of $G_2$, and then removing the identified edges. A
Brylawski, Chmutov, G. HETYEI, Y. DIAO
core +1 more source
, 2022 18 pages, 6 figures. This is a draft of a chapter for the Handbook on the Tutte Polynomial. Comments are welcome!
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Evaluations of Topological Tutte Polynomials [PDF]
Combinatorics, Probability and Computing, 2014 We find new properties of the topological transition polynomial of embedded graphs, Q(G). We use these properties to explain the striking similarities between certain evaluations of Bollobás and Riordan's ribbon graph polynomial, R(G), and the topological Penrose polynomial, P(G).
Ellis-Monaghan, J., Moffatt, I.
openaire +2 more sources
Splines, lattice points, and (arithmetic) matroids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Let $X$ be a $(d \times N)$-matrix. We consider the variable polytope $\Pi_X(u) = \left\{ w \geq 0 : Xw = u \right\}$. It is known that the function $T_X$ that assigns to a parameter $u \in \mathbb{R}^N$ the volume of the polytope $\Pi_X(u)$ is piecewise
Matthias Lenz
doaj +1 more source
Tetromino tilings and the Tutte polynomial [PDF]
, 2006 We consider tiling rectangles of size 4m x 4n by T-shaped tetrominoes. Each tile is assigned a weight that depends on its orientation and position on the lattice.
Baxter R J +8 more
core +6 more sources