Computes the Markov chain on k-bounded partitions (the set R_k) defined in:
The k-Plancherel measure and a Finite Markov Chain (with Svante Linusson), https://arxiv.org/abs/2512.24346
States are k-bounded partitions in R_k (|R_k| = k!), indexed via the factorial code. Transition probabilities follow the equation in Sect. 3.3 of the paper:
P(λ, μ) = d_μ^(k) / ((|λ|+1) · d_λ^(k))
where d_λ^(k) counts standard strong k-tableaux of shape c(λ), and μ is obtained from λ via a weak cover step on its (k+1)-core followed by rectangle reduction. All probabilities are computed as exact fractions.
python kcore_chain.py <k>Default is k=3. Output is saved to results/:
results/MC_<k>_frac.csv— transition matrix as exact fractionsresults/MC_<k>_float.csv— transition matrix as floats
Exact values obtained via separate computation for k = 3, 4, 5, 6 are available in the Data/ folder:
Data/transition_matrices/transition_matrix_k<k>.csv— transition matrix M_k as exact fractionsData/stationary_distributions/stationary_distribution_k<k>.csv— stationary distribution π_k as exact fractions
Python standard library only (fractions, math, collections, csv).