Related papers: Web matrices: structural properties and generating…
We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…
Analysing Web graphs has applications in determining page ranks, fighting Web spam, detecting communities and mirror sites, and more. This study is however hampered by the necessity of storing a major part of huge graphs in the external…
There are several ideas being used today for Web information retrieval, and specifically in Web search engines. The PageRank algorithm is one of those that introduce a content-neutral ranking function over Web pages. This ranking is applied…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…
We introduce a new class of combinatorial markets in which agents have covering constraints over resources required and are interested in delay minimization. Our market model is applicable to several settings including scheduling, cloud…
This paper serves as the first extension of the topic of dominator colorings of graphs to the setting of digraphs. We establish the dominator chromatic number over all possible orientations of paths and cycles. In this endeavor we discover…
Following Britz, Johnsen, Mayhew and Shiromoto, we consider demi\-ma\-troids as a(nother) natural generalization of matroids. As they have shown, demi\-ma\-troids are the appropriate combinatorial objects for studying Wei's duality. Our…
This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and…
Embeddings in AI convert symbolic structures into fixed-dimensional vectors, effectively fusing multiple signals. However, the nature of this fusion in real-world data is often unclear. To address this, we introduce two methods: (1)…
The classical Weisfeiler-Lehman method WL[2] uses edge colors to produce a powerful graph invariant. It is at least as powerful in its ability to distinguish non-isomorphic graphs as the most prominent algebraic graph invariants. It…
In here, I present a series of combinatorial equalities derived using a graph based approach. Different nodes in the graphs are visited following probabilistic dynamics of a moving dot. The results are presented in such a way that the…
Brualdi and Ma found a connection between involutions of length $n$ with $k$ descents and symmetric $k\times k$ matrices with non-negative integer entries summing to $n$ and having no row or column of zeros. From their main theorem they…
We introduce bud generating systems, which are used for combinatorial generation. They specify sets of various kinds of combinatorial objects, called languages. They can emulate context-free grammars, regular tree grammars, and synchronous…
We consider certain matrix-products where successive matrices in the product belong alternately to a particular qualitative class or its transpose. The main theorems relate structural and spectral properties of these matrix-products to the…
Lying at the interface between Network Science and Machine Learning, node embedding algorithms take a graph as input and encode its structure onto output vectors that represent nodes in an abstract geometric space, enabling various…
Two dimensional matrices with binary (0/1) entries are a common data structure in many research fields. Examples include ecology, economics, mathematics, physics, psychometrics and others. Because the columns and rows of these matrices…
We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…
Dynamical Ising machines achieve accelerated solving of complex combinatorial optimization problems by remapping the convergence to the ground state of the classical spin networks to the evolution of specially constructed continuous…
We study the statistical properties of the scattering matrix associated with generic quantum graphs. The scattering matrix is the quantum analogue of the classical evolution operator on the graph. For the energy-averaged spectral form…
We consider two problems that appear at first sight to be unrelated. The first problem is to count certain diagrams consisting of noncrossing arcs in the plane. The second problem concerns the weak order on the symmetric group. Each…