We show that SchÃ¼tzenbergerâ€™s promotion on two and three row rectangular Young tableaux can be realized as cyclic rotation of certain planar graphs introduced by Kuperberg. Moreover, following workâ€¦ (More)

We introduce a new class of " electrical " Lie groups. These Lie groups, or more precisely their nonnegative parts, act on the space of planar electrical networks via com-binatorial operationsâ€¦ (More)

We prove Stanleyâ€™s plethysm conjecture for the 2Ã—n case, which composed with the work of Black and List provides another proof of Foulkes conjecture for the 2Ã—n case. We also show that the wayâ€¦ (More)

This is the first of a series of papers where we develop a theory of total positivity for loop groups. In this paper, we completely describe the totally nonnegative part of the polynomial loop groupâ€¦ (More)

In combinatorics there is a well-known duality between non-nesting and non-crossing objects. In algebra there are many objects which are standard, for example Standard Young Tableaux, Standardâ€¦ (More)

For a directed graph G on vertices {0, bn) of non-negative integers such that, for every non-empty subset U âŠ† {1,. .. , n}, there exists a vertex j âˆˆ U for which there are more than bj edges goingâ€¦ (More)

Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, we study six combinatorial Hopf algebras. These Hopf algebras can be thought of as K-theoreticâ€¦ (More)

Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, we study six combinatorial Hopf algebras. These Hopf algebras can be thought of as K-theoreticâ€¦ (More)

We introduce the notion of the descent set polynomial as an alternative way of encoding the sizes of descent classes of permutations. Descent set polynomials exhibit interesting factorizationâ€¦ (More)