Related papers: Constructions and restrictions for balanced splitt…
We consider three matroids defined by Kalai in 1985: the symmetric completion matroid $\mathcal{S}_d$ on the edge set of a looped complete graph; the hyperconnectivity matroid $\mathcal{H}_d$ on the edge set of a complete graph; and the…
Structured matrices with symbolic sizes appear frequently in the literature, especially in the description of algorithms for linear algebra. Recent work has treated these symbolic structured matrices themselves as computational objects,…
We study examples of fourth-order Picard-Fuchs operators that are Hadamard products of two second-order Picard-Fuchs operators. Each second-order Picard-Fuchs operator is associated with a family of elliptic curves, and the Hadamard product…
Complex Hadamard matrices (CHMs) are intimately related to the number of distinct matrix elements. We investigate CHMs containing exactly three distinct elements, which is also the least number of distinct elements. In this paper, we show…
The density matrix of a qudit may be reconstructed with optimal efficiency if the expectation values of a specific set of observables are known. In dimension six, the required observables only exist if it is possible to identify six…
We comment on two randomized algorithms for constructing low-rank matrix decompositions. Both algorithms employ the Subsampled Randomized Hadamard Transform [14]. The first algorithm appeared recently in [9]; here, we provide a novel…
The NP-hard Distinct Vectors problem asks to delete as many columns as possible from a matrix such that all rows in the resulting matrix are still pairwise distinct. Our main result is that, for binary matrices, there is a complexity…
Daniel McNulty et.al (2024 J. Phys. A: Math. Theor. submitted) voiced suspicions to the Lemma 11(v) Part 6 in Chen and Yu (2017 J. Phys. A: Math. Theor. 50 475304) and three theorems derived in later publications (Liang et al 2019 Quantum…
Louis W. Shapiro gave a combinatorial proof of a bilinear generating function for Chebyshev polynomials equivalent to the formula 1/(1-ax-x^2) * 1/(1-bx-x^2) = (1-x^2)/(1-abx-(2+a^2+b^2)x^2 -abx^3+x^4), where * denotes the Hadamard product.…
A class of matroids is introduced which is very large as it strictly contains all paving matroids as special cases. As their key feature these split matroids can be studied via techniques from polyhedral geometry. It turns out that the…
Mating is an operation that identifies the domains of a polynomial pair in order to obtain a new map on the resulting quotient space. The dynamics of the mating are then dependent on the two polynomials and the manner in which the quotient…
Hashing plays an important role in information retrieval, due to its low storage and high speed of processing. Among the techniques available in the literature, multi-modal hashing, which can encode heterogeneous multi-modal features into…
This paper studies the properties of two kinds of matroids: (a) algebraic matroids and (b) finite and infinite matroids whose ground set have some canonical symmetry, for example row and column symmetry and transposition symmetry. For (a)…
Hadamard states were originally introduced for quantised Klein-Gordon fields and occupy a central position in the theory of quantum fields on curved spacetimes. Subsequently they have been developed for other linear theories, such as the…
We recognise Harada's generalized categories of diagrams as a particular case of modules over a monad defined on a finite direct product of additive categories. We work in the dual (albeit formally equivalent) situation, that is, with…
We describe properties of Hadamard products of algebraic varieties. We show any Hadamard power of a line is a linear space, and we construct star configurations from products of collinear points. Tropical geometry is used to find the degree…
In 2019, Perondi and Carmelo determined the set multipartite Ramsey number of particular complete bipartite graphs by establishing a relationship between the set multipartite Ramsey number, Hadamard matrices, and strongly regular graphs,…
This paper compares skew-linear and multilinear matroid representations. These are matroids that are representable over division rings and (roughly speaking) invertible matrices, respectively. The main tool is the von Staudt construction,…
We investigate the existence of heavy columns in binary matrices with distinct rows. A column of an m x n binary matrix is called heavy if the number of ones in it is at least m/2. We introduce two recursive algorithms, A1 and A2, that…
Over forty years ago, Goethals and Seidel showed that if the adjacency algebra of a strongly regular graph $X$ contains a Hadamard matrix then $X$ is either of Latin square type or of negative Latin square type. We extend their result to…