Combinatorial representation of tetrahedral chains

Ferroelectricity driven by twisting of silicate tetrahedral chains.

Combinatorial Representation Theory

We survey the field of combinatorial representation theory, describe the main results and main questions and give an update of its current status. Answers to the main questions are given in Part I for the fundamental structures, Sn and GL(n, C ), and later for certain generalizations, when known. Background material and more specialized results are given in a series of appendices. We give a per...

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...

Combinatorial Markov chains on linear extensions

We consider generalizations of Schützenberger's promotion operator on the set L of linear extensions of a finite poset of size n. This gives rise to a strongly connected graph on L. By assigning weights to the edges of the graph in two different ways, we study two Markov chains, both of which are irreducible. The stationary state of one gives rise to the uniform distribution, whereas the weight...

Daisy chains - a fruitful combinatorial concept

“Daisy, Daisy, give me your answer, do!” [10] For any positive integer n, the units of Zn are those elements of Zn \ {0} that are coprime with n. The number of units in Zn is given by Euler’s totient function φ(n). If n is odd, a daisy chain for the units of Zn is obtained by arranging the units of Zn on a circle in some order [a1, a2, . . . , aφ(n)] such that the set of differences bi = ai+1 −...