Slow Coupon Collecting under Fair Mechanisms

This repository contains all code used to generate the exact and numerical results in the paper

D. Barak‑Pelleg and D. Berend,
Fano Geometry and Slow Coupon Collecting.

The repository is intended as a reproducibility and data supplement to the paper.

Contents

• Exact recovery‑set enumeration for projective planes PG(2,q)
• Exact recovery‑set enumeration for affine planes AG(2,q)
• Exact expected coverage times via the Grunbaum–Yaakobi identity
• Monte Carlo simulations for larger parameters
• Exact and simulated full‑model baselines
• Exact computations for the star mechanism

Generating exact projective‑plane results

Run:

python3 compute_recovery_sets_PG.py

and enter the following values when prompted:

• (p, k) = (2, 1) to generate results for q = 2
• (p, k) = (3, 1) to generate results for q = 3
• (p, k) = (2, 2) to generate results for q = 4

The script produces the files:

• PG_q2.csv
• PG_q3.csv
• PG_q4.csv

Each CSV file contains the recovery‑set counts by size together with the exact expected coverage time (both as a rational number and as a decimal approximation).

Generating exact affine‑plane results

Analogously, run:

python3 compute_recovery_sets_AG.py

and enter the corresponding values of (p, k) to generate the files:

• AG_q2.csv
• AG_q3.csv
• AG_q4.csv

Notes

Exact recovery‑set enumeration is feasible only for small values of q (up to q = 4). Monte Carlo simulations for larger parameters may require up to 10^8 iterations and can take several hours.