Related papers: Combinatorial Representation Theory
We extend, in significant ways, the theory of truncated boolean representable simplicial complexes introduced in 2015. This theory, which includes all matroids, represents the largest class of finite simplicial complexes for which…
The study of combinatorial properties of mathematical objects is a very important research field and continued fractions have been deeply studied in this sense. However, multidimensional continued fractions, which are a generalization…
Many fundamental questions in theoretical computer science are naturally expressed as special cases of the following problem: Let $G$ be a complex reductive group, let $V$ be a $G$-module, and let $v,w$ be elements of $V$. Determine if $w$…
In this article, we study connections between representation theory and efficient solutions to the conjugacy problem on finitely generated groups. The main focus is on the conjugacy problem in conjugacy separable groups, where we measure…
Representation is a key notion in neuroscience and artificial intelligence (AI). However, a longstanding philosophical debate highlights that specifying what counts as representation is trickier than it seems. With this brief opinion paper…
We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.
The twenty-first century is a data-driven era where human activities and behavior, physical phenomena, scientific discoveries, technology advancements, and almost everything that happens in the world resulting in massive generation,…
Since its inception, the choice modelling field has been dominated by theory-driven modelling approaches. Machine learning offers an alternative data-driven approach for modelling choice behaviour and is increasingly drawing interest in our…
We discuss a general model for effective quantum field theories (QFTs), which for example comprises quantum chromodynamics and quantum electrodynamics. We assume in the model a perturbative expansion of the Lagrangian with respect to a…
These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students,…
We give an axiomatic framework for studying the representation theory of towers of algebras. We introduce a new class of algebras, contour algebras, generalising (and interpolating between) blob algebras and cyclotomic Temperley-Lieb…
In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String…
Matrix models and related Spin-Calogero-Sutherland models are of major relevance in a variety of subjects, ranging from condensed matter physics to QCD and low dimensional string theory. They are characterized by integrability and exact…
The combinatorial theory for the set of parity alternating permutations is expounded. In view of the numbers of ascents and inversions, several enumerative aspects of the set are investigated. In particular, it is shown that signed Eulerian…
The integral representation theorem for martingales has been widely used in probability theory. In this work, we propose and prove a general representation theorem for a class of set-valued submartingales. We also extend the stochastic…
This paper surveys the recent attempts, both from the machine learning and operations research communities, at leveraging machine learning to solve combinatorial optimization problems. Given the hard nature of these problems,…
Neural Combinatorial Optimization attempts to learn good heuristics for solving a set of problems using Neural Network models and Reinforcement Learning. Recently, its good performance has encouraged many practitioners to develop neural…
In recent years, representation learning has become the research focus of the machine learning community. Large-scale neural networks are a crucial step toward achieving general intelligence, with their success largely attributed to their…
Combinatorial interpretation of the fibonomial coefficients recently proposed by the present author results here in combinatorial interpretation of the recurrence relation for fibonomial coefficients . The presentation is provided with…
Performing machine learning on structured data is complicated by the fact that such data does not have vectorial form. Therefore, multiple approaches have emerged to construct vectorial representations of structured data, from kernel and…