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9 papers · 1 filter
Distinct Distances in Graph Drawings
Paz Carmi, Vida Dujmović, Pat Morin +1
The \emph{distance-number} of a graph is the minimum number of distinct edge-lengths over all straight-line drawings of in the plane. This definition generalises many well-…
A combinatorial formula for Macdonald polynomials
Arun Ram, Martha Yip
In this paper we use the combinatorics of alcove walks to give a uniform combinatorial formula for Macdonald polynomials for all Lie types. These formulas are generalizations of th…
Compatible Geometric Matchings
Oswin Aichholzer, Sergey Bereg, Adrian Dumitrescu +10
This paper studies non-crossing geometric perfect matchings. Two such perfect matchings are \emph{compatible} if they have the same vertex set and their union is also non-crossing.…
Rogers-Szego polynomials and Hall-Littlewood symmetric functions
S. Ole Warnaar
We use Rogers-Szego polynomials to unify some well-known identities for Hall-Littlewood symmetric functions due to Macdonald and Kawanaka.
Parametric production matrices and weighted succession rules: a Dyck path example
Robert Parviainen
We introduce weighted succession rules and parametric production matrices - simple extensions of the standard ECO method succession rules and production matrices. The purpose is to…
Area distribution and scaling function for punctured polygons
Christoph Richard, Iwan Jensen, Anthony J. Guttmann
Punctured polygons are polygons with internal holes which are also polygons. The external and internal polygons are of the same type, and they are mutually as well as self-avoiding…