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12 papers · 1 filter
A Short Proof of Gamas's Theorem
Andrew Berget
If χ^λis the irreducible character of the symmetric group S_n corresponding to the partition λof n then we may symmetrize a tensor v_1 \otimes ... \otimes v_n by χ^λ. Gamas's theor…
Positivity for cluster algebras from surfaces
Gregg Musiker, Ralf Schiffler, Lauren Williams
We give combinatorial formulas for the Laurent expansion of any cluster variable in any cluster algebra coming from a triangulated surface (with or without punctures), with respect…
Nonhomogeneous parking functions and noncrossing partitions
Drew Armstrong, Sen-Peng Eu
For each skew shape we define a nonhomogeneous symmetric function, generalizing a construction of Pak and Postnikov. In two special cases, we show that the coefficients of this fun…
Jack polynomials and the coinvariant ring of
Stephen Griffeth
We study the coinvariant ring of the complex reflection group as a module for the corresponding rational Cherednik algebra $\HH$ and its generalized graded affine Hecke…
The sorting order on a Coxeter group
Drew Armstrong
Let be an arbitrary Coxeter system. For each word in the generators we define a partial order--called the {\sf -sorting order}--on the set of group elements $W_ω\sub…
Geometry and complexity of O'Hara's algorithm
Matjaz Konvalinka, Igor Pak
In this paper we analyze O'Hara's partition bijection. We present three type of results. First, we show that O'Hara's bijection can be viewed geometrically as a certain scissor con…