Combinatorial Representation Theory

Combinatorial Representation Theory of Lie Algebras. Richard Stanley’s Work and the Way It Was Continued

Representation theory is a fundamental tool for studying group symmetry − geometric, analytic, or algebraic − by means of linear algebra, which has important applications to other areas of mathematics and mathematical physics. One very successful trend in this field in recent decades involves using combinatorial objects to model the representations, which allows one to apply combinatorial metho...

Advanced Graph Theory and Combinatorial Optimization

Advanced Graph Theory and Combinatorial Optimization Contents

Nathaniel Thiem Combinatorial representation theory

My primary research interest is in the interplay between combinatorics and algebraic structures. By employing combinatorial tools such as symmetric functions, partitions, tableaux, graphs, posets, and crystal bases, one can gain significant insight on algebraic and geometric structures such as groups, algebras and rings; and, conversely, the corresponding structure theory can often lead to surp...

A generalization of the probability that the commutator of two group elements is equal to a given element

The probability that the commutator of two group elements is equal to a given element has been introduced in literature few years ago. Several authors have investigated this notion with methods of the representation theory and with combinatorial techniques. Here we illustrate that a wider context may be considered and show some structural restrictions on the group.

Half-Century Journey from Synthetic Organic Chemistry to Mathematical Stereochemistry through Chemoinformatics

My half-century journey started from synthetic organic chemistry. During the first stage of my journey, my interest in stereochemistry was initiated through the investigation on the participation of steric effects in reactive intermediates, cylophanes, strained heterocycles, and organic compounds for photography. In chemoinformatics as the next stage of the journey, I proposed the concept of im...