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Combinatorial Hopf algebras and K-homology of Grassmanians
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-theoreticExpand
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Promotion and cyclic sieving via webs
We show that Schützenberger’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 workExpand
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Laurent phenomenon algebras
We generalize Fomin and Zelevinsky's cluster algebras by allowing exchange polynomials to be arbitrary irreducible polynomials, rather than binomials.
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Tensor diagrams and cluster algebras
The rings of SL(V) invariants of configurations of vectors and linear forms in a finite-dimensional complex vector space V were explicitly described by Hermann Weyl in the 1930s. We show that when VExpand
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A family of bijections between G-parking functions and spanning trees
For a directed graph G on vertices {0, 1, ..., n}, a G-parking function is an n-tuple (b1,...,bn) of non-negative integers such that, for every non-empty subset U ⊆ {1,...,n}, there exists a vertex jExpand
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Electrical networks and Lie theory
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 combinatorial operationsExpand
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Total positivity in loop groups I: whirls and curls
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 groupExpand
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A non-crossing standard monomial theory
The second author has introduced non-crossing tableaux, objects whose non-nesting analogues are semi-standard Young tableaux. We relate non-crossing tableaux to Gelfand-Tsetlin patterns and developExpand
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Inverse Problem in Cylindrical Electrical Networks
In this paper we study the inverse Dirichlet-to-Neumann problem for certain cylindrical electrical networks. We define and study a birational transformation acting on cylindrical electrical networksExpand
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Dual Filtered Graphs
We define a K-theoretic analogue of Fomin's dual graded graphs, which we call dual filtered graphs. The key formula in the definition is DU-UD= D + I. Our major examples are K-theoretic analogues ofExpand
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