Graduate Projects
Here is a collection of some of my graduate projects, past and present.
This page mainly serves as a file share for my collaborators, some crucial files and project details may be missing.
Statistical Properties of Permutations and SYT reflected by the Robinson-Schensted Algorithm:
Paper & Slides
Full written paper covering all four experimental directions: the Logan-Shepp limit shape and convergence of λ1/√n to 2; covariance and correlation between longest increasing and decreasing subsequence lengths; location statistics of a fixed entry m in the insertion and recording tableaux and the asymptotic independence conjecture; and row/column sum vector uniqueness questions for standard Young tableaux with novel integer sequences.
- Authors: Austin DeCicco, Jike Liu
- Last Updated: May 7, 2026
Beamer slides for the course presentation. Walks through background on the RS bijection, Schensted's theorem, Plancherel measure, and all four experimental sections of the paper.
- Last Updated: May 7, 2026
Maple Code
Single file containing every Maple procedure used across the project, consolidated from all source files. Covers the core RS implementation, longest subsequence routines, dataset generation, Schensted's theorem verification, Logan-Shepp plotting, first-row/first-column Monte Carlo, the asymptotic independence rate tests, the average shape bootstrap, and all row/column sum brute-force procedures. Short descriptions are provided in comments above each procedure, with sample commands at the bottom of the file.
- Last Updated: May 7, 2026
Datasets
The base dataset for the project. Saves the variable Q, where
Q[n][j] is a pair [π, [P, Q]] — a uniformly
sampled permutation from Sn together with its full RS output,
both tableaux. Covers n = 1 to 30 with up to 3000 observations per
n (exact enumeration for small n). All other datasets are derived
from this one.
- Last Updated:May 7, 2026
Saves the variable AvgShape, a bootstrap summary of RS shape
statistics. AvgShape[1][n] is the component-wise sample mean of
the shape vector of P over 3000 bootstrap samples at each n from
1 to 30, and AvgShape[2][n] is the corresponding standard error.
Used for the row-removal heuristic experiments in Section 5 of the paper via
AvgnthLength(x), senthLength(x), and
TestProposition().
- Last Updated: May 7, 2026
Saves the variable InDeQ, a flat list of pairs
[LIS length, LDS length] = [λ1,
λ'1] extracted from every permutation in
RSDataset, ordered by n from 1 to 30. Used by
SubseqCov() to compute the sample covariance of Rn
and Cn at each n, supporting the conjectures in
Section 4 of the paper.
- Last Updated: May 7, 2026
Saves the variable BRCN, a bootstrap summary of row and column
sum vector statistics. BRCN[i][n] is indexed by statistic type
i and permutation size n (1 to 30): the eight entries cover the
sample mean and standard error of the row sum vector and column sum vector for
both P and Q, each averaged over 3000 bootstrap samples. Used
for the row/column sum uniqueness experiments in Section 7 of the paper.
- Last Updated: May 7, 2026