相关论文: Every non-Euclidean oriented matroid admits a biqu…
We provide a full classification of all families of matroids that are closed under duality and minors, and for which the Tutte polynomial is a universal valuative invariant. There are four inclusion-wise maximal families, two of which are…
We prove that for each finite field $\mathbb F$ and integer $k\in \mathbb Z$ there exists $n\in \mathbb Z$ such that no excluded minor for the class of $\mathbb F$-representable matroids has $n$ nested $k$-separations.
We prove that there is no polynomial $p(\cdot)$ with the property that a matroid $M$ can be determined to be either a lifted-graphic or frame matroid using at most $p(|M|)$ rank evaluations. This resolves two conjectures of Geelen, Gerards…
We prove that any unicritical polynomial $f_c:z\mapsto z^d+c$ which is at most finitely renormalizable and has only repelling periodic points is combinatorially rigid. It implies that the connectedness locus (the ``Multibrot set'') is…
We present an example of a fibred quadratic polynomial admitting an attracting invariant 2-curve. By an unfolding construction we obtain an example of a fibred quadratic polynomial admitting two attracting invariant curves. This phenomena…
In this paper, we give a new axioms system based on nonseparable flats with their ranks to define a matroid. We deduce a polynomial time algorithm for deciding if a given matroid (respectively, arbitrary structure) is an uniform matroid.…
H. J. S. Smith proved Fermat's two-square theorem using the notion of palindromic continuants. In this paper we extend Smith's approach to proper binary quadratic form representations in some commutative Euclidean rings, including rings of…
We prove that a cuspidal automorphic representation of GL(3) over any number field is determined by the quadratic twists of its central value. In the case of a non-Gelbart-Jacquet lift, the result is conditional on the analytic behavior of…
We show that no minimal vertex triangulation of a closed, connected, orientable 2-manifold of genus 6 admits a polyhedral embedding in R^3. We also provide examples of minimal vertex triangulations of closed, connected, orientable…
We establish the equidistribution with respect to the bifurcation measure of post-critically finite maps in any one-dimensional algebraic family of unicritical polynomials. Using this equidistribution result, together with a combinatorial…
In 2010, Izhakian & Margolis proved that the bicyclic monoid admits a representation as a semigroup of upper triangular tropical matrices. We extend this result by classifying all one-relation monoids which admit such representations. We…
In this paper we prove the existence and uniqueness of matings of the basilica with any quadratic polynomial which lies outside of the 1/2-limb of M, is non-renormalizable, and does not have any non-repelling periodic orbits.
The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…
We show that the linear coefficient of the Ehrhart polynomial of a matroid base polytope evaluated at $t-1$ is equal to, up to normalization, the $\beta$-invariant of the matroid. This yields a lattice-point counting formula for the…
The fundamental theorem of symmetric polynomials over rings is a classical result which states that every unital commutative ring is fully elementary, i.e. we can express symmetric polynomials with elementary ones in a unique way. The…
We prove that if $ M $ and $ N $ are finitary matroids on a common countable edge set $ E $ then they admit a common independent set $I $ such that there is a bipartition $ E=E_{M}\cup E_{N} $ for which $ I\cap E_M $ spans $ E_M $ in $ M $…
We discuss a recent result by C. Culter: every polygonal outer billiard has a periodic trajectory.
The equivariant Kazhdan-Lusztig polynomial of a matroid was introduced by Gedeon, Proudfoot, and Young. Gedeon conjectured an explicit formula for the equivariant Kazhdan-Lusztig polynomials of thagomizer matroids with an action of…
We provide a short proof of a conic version of the colorful Carath\'eodory theorem for oriented matroids. Holmsen's extension of the colorful Carath\'eodory theorem to oriented matroids (Advances in Mathematics, 2016) already encompasses…
We study algebraic properties of the Tutte polynomial of a matroid and its generalizations to other combinatorially defined bivariate polynomial invariants. Merino, de Mier and Noy showed that the Tutte polynomial of a connected matroid is…