Related papers: Gorenstein graphic matroids from multigraphs
Hypertoric varieties are quaternionic analogues of toric varieties, important for their interaction with the combinatorics of matroids as well as for their prominent place in the rapidly expanding field of algebraic symplectic and…
In this work we provide a decomposition theorem for the class of quaternary and non-binary signed-graphic matroids. This generalizes previous results for binary signed-graphic matroids and graphic matroids, and it provides the theoretical…
We define a simple orthogonal polyhedron to be a three-dimensional polyhedron with the topology of a sphere in which three mutually-perpendicular edges meet at each vertex. By analogy to Steinitz's theorem characterizing the graphs of…
Given a subgroup $\mathcal{H}$ of a product of finite groups $\mathcal{G} = \displaystyle\prod^n_{i=1} \Gamma_i$ and $b>1,$ we define a polymatroid $P(\mathcal{H},b).$ If all of the $\Gamma_i$ are isomorphic to $\mathbb{Z}/p\mathbb{Z},$ $p$…
We present and study the concept of $m$-periodic Gorenstein objects relative to a pair $(\mathcal{A,B})$ of classes of objects in an abelian category, as a generalization of $m$-strongly Gorenstein projective modules over associative rings.…
In this paper, we introduce the concept of the weighted (harmonic) chromatic polynomials of graphs and discuss some of its properties. We also present the notion of the weighted (harmonic) Tutte--Grothendieck polynomials of graphs and give…
The Topological Representation Theorem for (oriented) matroids states that every (oriented) matroid can be realized as the intersection lattice of an arrangement of codimension one homotopy spheres on a homotopy sphere. In this paper, we…
We establish restrictions on the Hilbert function of standard graded Gorenstein algebras with only quadratic relations. Furthermore, we pose some intriguing conjectures and provide evidence for them by proving them in some cases using a…
One of the most important classes of even $\Delta$-matroids arises from orientable ribbon graphs, which play a role analogous to that of graphic matroids in matroid theory. Motivated by a natural correspondence between strong…
A matroid is supersolvable if it has a maximal chain of flats each of which is modular. A matroid is saturated if every round flat is modular. In this article we present supersolvable saturated matroids as analogues to chordal graphs, and…
A recent line of research has concentrated on exploring the links between analytic and combinatorial theories of submodularity, uncovering several key connections between them. In this context, Lov\'asz initiated the study of matroids from…
In this note we introduce a sufficient condition for the Orlik-Solomon algebra associated to a matroid M to be l-adic and we prove that this condition is necessary when M is binary (in particular graphic). Moreover, this result cannot be…
A matroid is $\text{GF}(q)$-regular if it is representable over all proper superfields of the field $\text{GF}(q)$. We show that, for highly connected matroids having a large projective geometry over $\text{GF}(q)$ as a minor, the property…
A graph H is common if the number of monochromatic copies of H in a 2-edge-colouring of the complete graph is minimised by the random colouring. Burr and Rosta, extending a famous conjecture by Erdos, conjectured that every graph is common.…
The study of the $h$-vectors of graded Gorenstein algebras is an important topic in combinatorial commutative algebra, which despite the large amount of literature produced during the last several years, still presents many interesting open…
Zaslavsky introduced the concept of lifted-graphic matroid. For binary matroids, a binary elementary lift can be defined in terms of the splitting operation. In this paper, we give a method to get a forbidden-minor characterization for the…
We give a common matroidal generalisation of `A Cantor-Bernstein theorem for paths in graphs' by Diestel and Thomassen and `A Cantor-Bernstein-type theorem for spanning trees in infinite graphs' by ourselves.
We classify exactly when the toric algebras $\C[S_{\tree}(\br)]$ are Gorenstein. These algebras arise as toric deformations of algebras of invariants of the Cox-Nagata ring of the blow-up of $n-1$ points on $\mathbb{P}^{n-3}$, or…
In this work, we are concerned with hierarchically hyperbolic spaces and hierarchically hyperbolic groups. Our main result is a wide generalization of a combination theorem of Behrstock, Hagen, and Sisto. In particular, as a consequence, we…
A G-gain graph is a graph whose oriented edges are labeled invertibly from a group G. Zaslavsky proposed two matroids of G-gain graphs, called frame matroids and lift matroids, and investigated linear representations of them. Each matroid…