Related papers: Sweep maps: A continuous family of sorting algorit…
Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors…
Recursive coalgebras provide an elegant categorical tool for modelling recursive algorithms and analysing their termination and correctness. By considering coalgebras over categories of suitably indexed families, the correctness of the…
We present an algorithmic equivalent statement to the Jacobian conjecture. Given a polynomial map F on an affine space of dimension n, our algorithm constructs n sequences of polynomials such that F is invertible if and only if the zero…
We study the ramification divisors of projections of a smooth projective variety onto a linear subspace of the same dimension. We prove that the ramification divisors vary in a maximal dimensional family for a large class of varieties.…
This paper introduces combinatorial representations, which generalise the notion of linear representations of matroids. We show that any family of subsets of the same cardinality has a combinatorial representation via matrices. We then…
This is a book on higher-categorical diagrams, including pasting diagrams. It aims to provide a thorough and modern reference on the subject, collecting, revisiting and expanding results scattered across the literature, informed by recent…
We present an exact and efficient algorithm for computing the Reeb space of a bivariate PL map. The Reeb space is a topological structure that generalizes the Reeb graph to the setting of multiple scalar-valued functions defined over a…
Subtraction schemes provide a systematic way to compute fully-differential cross sections beyond the leading order in the strong coupling constant. These methods make singular real-emission corrections integrable in phase space by the…
For a natural class of $r \times n$ integer matrices, we construct a non-convex polytope which periodically tiles $\mathbb R^n$. From this tiling, we provide a family of geometrically meaningful maps from a generalized sandpile group to a…
The quest for efficient sorting is ongoing, and we will explore a graph-based stable sorting strategy, in particular employing comparison graphs. We use the topological sort to map the comparison graph to a linear domain, and we can…
Sampling-based algorithms solve the path planning problem by generating random samples in the search-space and incrementally growing a connectivity graph or a tree. Conventionally, the sampling strategy used in these algorithms is biased…
This paper is concerned with the complexity analysis of constructor term rewrite systems and its ramification in implicit computational complexity. We introduce a path order with multiset status, the polynomial path order POP*, that is…
We consider maps on genus-$g$ surfaces with $n$ (labeled) faces of prescribed even degrees. It is known since work of Norbury that, if one disallows vertices of degree one, the enumeration of such maps is related to the counting of lattice…
We present, to the best of the authors' knowledge, all known results for the (planar) crossing numbers of specific graphs and graph families. The results are separated into various categories; specifically, results for general graph…
Given a smooth, open, oriented surface $X$ endowed with a family of complex structures $\{J_b\}_{b\in B}$ depending continuously on the parameter $b$ in a metrisable space $B$, we construct a continuous family of proper holomorphic maps…
We present a novel technique for constructing differentiable order-type operations, including soft ranking, soft top-k selection, and soft permutations. Our approach leverages an efficient closed-form formula for the inverse of the function…
We introduce a family of univariate polynomials indexed by integer partitions. At prime powers, they count the number of subspaces in a finite vector space that transform under a regular diagonal matrix in a specified manner. This…
Reeb graphs are widely used in a range of fields for the purposes of analyzing and comparing complex spaces via a simpler combinatorial object. Further, they are closely related to extended persistence diagrams, which largely but not…
We introduce certain lattice sums associated with hyperplane arrangements, which are (multiple) sums running over integers, and can be regarded as generalizations of certain linear combinations of zeta-functions of root systems. We also…
Covering is a common type of data structure and covering-based rough set theory is an efficient tool to process this data. Lattice is an important algebraic structure and used extensively in investigating some types of generalized rough…