Grothendieck shenanigans - simulation of random permutations from staircase reduced word permutations
Leonid Petrov
Displays a permutation matrix as a scatter plot of dots, where each dot represents a fixed point mapping. Simulates random permutations from staircase reduced words via nonsymmetric Grothendieck polynomials. Adjust size N (up to 20000), probability p, and parameter q with sliders and arrow buttons, then click Change N to regenerate.
This page simulates random permutations arising from nonsymmetric
Grothendieck polynomials. For more details, see our paper
[45].
Use the controls below to choose $N$, $p$, and $q$,
then view the resulting permutation matrix drawn via D3.js.
Simulation Controls
1000
The initial pipe dream boundary condition (where the pipe dreams live) is as follows:
code
(note: parameters in the code might differ from the ones in simulation results below)-
Link to code(This simulation is interactive, written in JavaScript, see the source code of this page at the link) -
Link to code(c code for the simulation of heatmaps, runs faster)