13 citations · 31 across the 10 of their papers we have counts for
12 papers · 1 filter
Sweep maps: A continuous family of sorting algorithms
Drew Armstrong, Nicholas A. Loehr, Gregory S. Warrington
We define a family of maps on lattice paths, called sweep maps, that assign levels to each step in the path and sort steps according to their level. Surprisingly, although sweep ma…
Rational parking functions and Catalan numbers
Drew Armstrong, Nicholas A. Loehr, Gregory S. Warrington
The classical parking functions, counted by the Cayley number (n+1)^(n-1), carry a natural permutation representation of the symmetric group S_n in which the number of orbits is th…
Results and conjectures on simultaneous core partitions
Drew Armstrong, Christopher R. H. Hanusa, Brant C. Jones
An n-core partition is an integer partition whose Young diagram contains no hook lengths equal to n. We consider partitions that are simultaneously a-core and b-core for two relati…
Rational associahedra and noncrossing partitions
Drew Armstrong, Brendon Rhoades, Nathan Williams
Each positive rational number x>0 can be written uniquely as x=a/(b-a) for coprime positive integers 0<a<b. We will identify x with the pair (a,b). In this paper we define for each…
Parking Spaces
Drew Armstrong, Victor Reiner, Brendon Rhoades
Let be a Weyl group with root lattice and Coxeter number . The elements of the finite torus are called the -{\sf parking functions}, and we call the permut…
A uniform bijection between nonnesting and noncrossing partitions
Drew Armstrong, Christian Stump, Hugh Thomas
In 2007, D.I. Panyushev defined a remarkable map on the set of nonnesting partitions (antichains in the root poset of a finite Weyl group). In this paper we identify Panyushev's ma…