Related papers: Encoding labelled $p$-Riordan graphs by words and …

We enumerate the fibres of commutator word maps over p-groups of nilpotency class less than p with exponent p. We also give some examples and enumerate the fibre sizes of all word maps over p-groups of class 2 with exponent p.

The automaton transformation of infinite words over alphabet $\mathbb F_p=\{0,1,\ldots,p-1\}$, where $p$ is a prime number, coincide with the continuous transformation (with respect to the $p$-adic metric) of a ring $\mathbb Z_p$ of…

A recent paper by Drewes, Hoffmann, and Minas (GCM 2023 proceedings) has shown that certain graph languages can be defined and efficiently recognized by finite automata when strings over typed symbols are interpreted as graphs. This…

Learning knowledge graph embedding from an existing knowledge graph is very important to knowledge graph completion. For a fact $(h,r,t)$ with the head entity $h$ having a relation $r$ with the tail entity $t$, the current approaches aim to…

We use the classical umbral calculus to describe Riordan arrays. Here, a Riordan array is generated by a pair of umbrae, and this provides efficient proofs of several basic results of the theory such as the multiplication rule, the…

This paper investigates data-driven segmentation using Re-Pair or Byte Pair Encoding-techniques. In contrast to previous work which has primarily been focused on subword units for machine translation, we are interested in the general…

Ribbon graphs embedded on a Riemann surface provide a useful way to describe the double line Feynman diagrams of large N computations and a variety of other QFT correlator and scattering amplitude calculations, e.g in MHV rules for…

P systems are computing conceptual computing devices that are at least as powerful as Turing machines. However, until recently it was not known how one can encode any recursive function as a P~system. Here we propose a new encoding of…

Multi-hop reading comprehension across multiple documents attracts much attention recently. In this paper, we propose a novel approach to tackle this multi-hop reading comprehension problem. Inspired by human reasoning processing, we…

The class of Parikh word representable graphs were recently introduced. In this work, we further develop its general theory beyond the binary alphabet. Our main result shows that this class is equivalent to the class of bipartite…

For an integer $p\geq 2$ we construct vertical and horizontal one-pth Riordan arrays from a Riordan array. When $p=2$, one-pth Riordan arrays reduced to well known half Riordan arrays. The generating functions of the $A$-sequences of…

A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $(x,y)\in E$. A triangular grid graph is a subgraph of a tiling of the plane with…

We propose a fast methodology for encoding graphs with information-theoretically minimum numbers of bits. Specifically, a graph with property pi is called a pi-graph. If pi satisfies certain properties, then an n-node m-edge pi-graph G can…

The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…

In this work, we investigate the relationship between $k$-repre\-sentable graphs and graphs representable by $k$-local words. In particular, we show that every graph representable by a $k$-local word is $(k+1)$-representable. A previous…

Combining the message-passing paradigm with the global attention mechanism has emerged as an effective framework for learning over graphs. The message-passing paradigm and the global attention mechanism fundamentally generate node…

The family of graphs of reduced words of a certain subcollection of permutations in the union $\cup_{n\geq 4}\frak{S}_{n}$ of symmetic groups is investigated. The subcollection is characterised by the hook cycle type $(n-2,1,1)$ with…

The Fibonacci cube $\Gamma_n$ is the subgraph of the hypercube $Q_n$ induced by vertices with no consecutive $1$s. Recently Jianxin Wei and Yujun Yang introduced a one parameter generalization, Fibonacci $p$-cubes $\Gamma_n^p$, which are…

In [1] M. Baker and S. Norine developed a theory of divisors and linear systems on graphs, and proved a Riemann-Roch Theorem for these objects (conceived as integer-valued functions on the vertices). In [2] and [3] the authors generalized…

In this paper, we study the word-representability of well-partitioned chordal graphs using split decomposition. We show that every component of the minimal split decomposition of a well-partitioned chordal graph is a split graph. Thus we…