相关论文: A new labeling construction from the $\otimes_h$-p…

This is a rather personal introductory outline of an interesting class of geometric, resp. graph- and group-theoretical structures. After an introductive section about their genesis, the general construction of horocyclic products is…

We describe how to construct and enumerate Magic squares, Franklin squares, Magic cubes, and Magic graphs as lattice points inside polyhedral cones using techniques from Algebraic Combinatorics. The main tools of our methods are the Hilbert…

Clustering aims to group unlabelled samples based on their similarities. It has become a significant tool for the analysis of high-dimensional data. However, most of the clustering methods merely generate pseudo labels and thus are unable…

We prove that every holomorphic symplectic matrix can be factorized as a product of holomorphic unitriangular matrices with respect to the symplectic form $ \left[\begin{array}{ccc} 0 & L_n \\ -L_n & 0\end{array}\right]$ where $L$ is the $n…

Superconformal indices of four-dimensional $\mathcal{N}=1$ gauge theories factorize into holomorphic blocks. We interpret this as a modular property resulting from the combined action of an $SL(3,\mathbb{Z})$ and $SL(2,\mathbb{Z})\ltimes…

Automated label generation for clusters of scientific documents is a common task in bibliometric workflows. Traditionally, labels were formed by concatenating distinguishing characteristics of a cluster's documents; while straightforward,…

Product structure theorems are a collection of recent results that have been used to resolve a number of longstanding open problems on planar graphs and related graph classes. One particularly useful version states that every planar graph…

Let A be a central simple algebra over a field F. Let k_1,\ldots, k_r be cyclic extensions of F such that k_1\otimes_F\cdots \otimes_F k_r is a field. We investigate conditions under which A is a tensor product of symbol algebras where each…

Product classification is the task of automatically predicting a taxonomy path for a product in a predefined taxonomy hierarchy given a textual product description or title. For efficient product classification we require a suitable…

This manuscript introduces a general multisection identity expressed equivalently in terms of infinite double products and/or infinite double series, from which several new product or summation identities involving special functions…

Families of codes such as group codes, constacyclic and skew cyclic codes, some of which independently suggested in the literature, turn out to be special instances of the general family of crossed product codes. Hamming-metric is a main…

The geometric product, defined by Graf on the space of differential forms, endows the sections of the exterior bundle by a structure that is necessary to construct a Clifford algebra. The Graf product is introduced and revisited with a…

We demonstrate that a modification of the classical index calculus algorithm can be used to factor integers. More generally, we reduce the factoring problem to finding an overdetermined system of multiplicative relations in any factor base…

We show that the ordinary cohomology functor from the category of augmented $k$-algebras to itself exchanges coproducts and products, and that Hochschild cohomology is close to sending coproducts to products if the factors are…

Dirichlet's $L$-functions are natural extensions of the Riemann zeta function. In this paper we first give a brief survey of Ap\'ery-like series for some special values of the zeta function and certain $L$-functions. Then, we establish two…

We present new combinatorial objects, which we call grid-labelled graphs, and show how these can be used to represent the quantum states arising in a scenario which we refer to as the faulty emitter scenario: we have a machine designed to…

Tensor network diagram (graphical notation) is a useful tool that graphically represents multiplications between multiple tensors using nodes and edges. Using the graphical notation, complex multiplications between tensors can be described…

Products of shifted characteristic polynomials, and ratios of such products, averaged over the classical compact groups are of great interest to number theorists as they model similar averages of L-functions in families with the same…

Power-type graphs, such as the power graph, the directed power graph, the enhanced power graph and the difference graph, encode significant information about the internal structure of a finite group. Despite substantial investigation in…

In this paper, we study some new factorizations of period-doubling sequences over a $k$-letter alphabet, where $k\geq 2$. First, we define the combinatorial and arithmetic properties of these sequences. Then, we define the kernel words of…