Related papers: Lattice path matroids and quotients
Discrete polymatroids are the multi-set analogue of matroids. In this paper, we explore the connections among linear network coding, linear index coding and representable discrete polymatroids. We consider vector linear solutions of…
In this article we make several contributions of independent interest. First, we introduce the notion of stressed hyperplane of a matroid, essentially a type of cyclic flat that permits to transition from a given matroid into another with…
The lattice cell in the ${i+1}^{st}$ row and ${j+1}^{st}$ column of the positive quadrant of the plane is denoted $(i,j)$. If $\mu$ is a partition of $n+1$, we denote by $\mu/ij$ the diagram obtained by removing the cell $(i,j)$ from the…
It is known that a lattice path matroid polytope can be associated with two given noncrossing lattice paths on $\mathbb{Z}\times\mathbb{Z}$ with the same end points. In this short note we give explicit formulae for the $f$-vector, toric…
There has been significant interest in studying the asymptotics of certain generalised moments, called the moments of moments, of characteristic polynomials of random Haar-distributed unitary and symplectic matrices, as the matrix size $N$…
In this paper, we investigate the relation between a $q$-matroid and its associated matroid called the projectivization matroid. The latter arises by projectivizing the groundspace of the $q$-matroid and considering the projective space as…
Wilson loop diagrams are an important tool in studying scattering amplitudes of SYM $N=4$ theory and are known by previous work to be associated to positroids. We characterize the conditions under which two Wilson loop diagrams give the…
We give a criterion which characterizes a real multi-variate Laurent polynomial with full-dimensional smooth Newton polytope to have the property that all sufficiently large powers of the polynomial have fully positive coefficients. Here a…
We are interested in expanding our understanding of symplectic matroids by exploring the properties of a class of symplectic matroids with a "lattice of flats". Taking a well-behaved family of subdivisions of the cross polytope we obtain a…
Using the framework of pastures and foundations of matroids developed by Baker-Lorscheid, we give algorithms to: (i) compute the foundation of a matroid, and (ii) compute all morphisms between two pastures. Together, these provide an…
We evaluate the configuration exponents of various ensembles of Hamiltonian paths drawn on random planar bicubic maps. These exponents are estimated from the extrapolations of exact enumeration results for finite sizes and compared with…
We give a deterministic polynomial time $2^{O(r)}$-approximation algorithm for the number of bases of a given matroid of rank $r$ and the number of common bases of any two matroids of rank $r$. To the best of our knowledge, this is the…
The aim of this paper is to study lattice properties of the sharp partial order for complex matrices having index at most 1. We investigate the down-set of a fixed matrix $B$ under this partial order via isomorphisms with two different…
The LLT polynomials $\mathcal{L}_{\mathbf{\beta}/\mathbf{\gamma}} (X;t)$ are a family of symmetric polynomials indexed by a tuple of (possibly skew-)partitions $\mathbf{\beta}/\mathbf{\gamma}=…
Motivated by the notion of the inverse $Z$-polynomial introduced by Ferroni, Matherne, Stevens, and Vecchi, we study the equivariant inverse $Z$-polynomial of a matroid equipped with a finite group. We prove that the coefficients of the…
In 2004, Choe, Oxley, Sokal and Wagner established a tight connection between matroids and multiaffine real stable polynomials. Recently, Branden used this theory and a polynomial coming from the Vamos matroid to disprove the generalized…
We find a bijection between bi-banded paths and peak-counting paths, applying to two classes of lattice paths including Dyck paths. Thus we find a new interpretation of Narayana numbers as coefficients of weight polynomials enumerating…
Motivated by the characterization of the lattice of cyclic flats of a matroid, the convolution of a ranked lattice and a discrete measure is defined, generalizing polymatroid convolution. Using the convolution technique we prove that if a…
Let M be a matroid on ground set E. A subset l of E is called a `line' when its rank equals 1 or 2. Given a set L of lines, a `fractional matching' in (M,L) is a nonnegative vector x indexed by the lines in L, that satisfies a system of…
The Chow class of the closure of the torus orbit of a point in a Grassmannian only depends on the matroid associated to the point. The Chow class can be extended to a matroid invariant of arbitrary matroids. We call the coefficients…