Related papers: Ramanujan Complexes and High Dimensional Expanders

In the present paper, we introduce a multiple Ramanujan sum for arithmetic functions, which gives a multivariable extension of the generalized Ramanujan sum studied by D. R. Anderson and T. M. Apostol. We then find fundamental arithmetic…

Graph processing is becoming increasingly prevalent across many application domains. In spite of this prevalence, there is little research about how graphs are actually used in practice. We performed an extensive study that consisted of an…

We discuss several topics related to polylogarithms with focus on dilogarithms. The topics are: a generating function with harmonic numbers coming from Ramanujan, extending the dilogarithm to complex numbers beyond the unit disk, and…

Graphs are by nature unifying abstractions that can leverage interconnectedness to represent, explore, predict, and explain real- and digital-world phenomena. Although real users and consumers of graph instances and graph workloads…

Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…

This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…

Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…

In this paper we introduce a path complex that can be regarded as a generalization of the notion of a simplicial complex. The main motivation for considering path complexes comes from directed graphs(digraphs). We obtain a new notion of the…

Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…

Ramanujan's Master Theorem is a decades-old theorem in the theory of Mellin transforms which has wide applications in both mathematics and high energy physics. The unconventional method of Ramanujan in his proof of the theorem left…

In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion complexity. In this paper, we slightly modify this notion to obtain the so-called irreducible-expansion complexity which is more suitable for…

Simplicial complexes are extensively studied in the field of algebraic topology. They have gained attention in recent time due to their applications in fields like theoretical distributed computing and simplicial neural networks. Graphs are…

Dynamic graph learning has gained significant attention as it offers a powerful means to model intricate interactions among entities across various real-world and scientific domains. Notably, graphs serve as effective representations for…

Graph neural networks provide a powerful toolkit for embedding real-world graphs into low-dimensional spaces according to specific tasks. Up to now, there have been several surveys on this topic. However, they usually lay emphasis on…

Graph is a well known data structure to represent the associated relationships in a variety of applications, e.g., data science and machine learning. Despite a wealth of existing efforts on developing graph processing systems for improving…

We introduce a new combinatorial abstraction for the graphs of polyhedra. The new abstraction is a flexible framework defined by combinatorial properties, with each collection of properties taken providing a variant for studying the…

For a simplicial complex $\Delta$, we introduce a simplicial complex attached to $\Delta$, called the expansion of $\Delta$, which is a natural generalization of the notion of expansion in graph theory. We are interested in knowing how the…

We present applications of rectangular matrix models to various combinatorial problems, among which the enumeration of face-bicolored graphs with prescribed vertex degrees, and vertex-tricolored triangulations. We also mention possible…

We revisit several entries from Ramanujan's notebooks which follow from more elementary arguments than a first glance may suggest. Our goal is to demystify these results through more accessible proofs, while also shining some light on the…

In this paper, we use the theory of Riordan matrices to introduce the notion of a Riordan graph. The Riordan graphs are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other…