Timeline

Complete rewrite with three pillars: isolated sign benchmarks, formal parallel-complexity analysis (factorial tree, span $O(n)$ vs the chains' $\Omega(n!)$ critical path), and vectorized implementations with benchmarks. Zenodo record (DOI 10.5281/zenodo.21326563).

Vectorized meryemPer generates all permutations up to 6× faster than the C-implemented itertools chain; all 479,001,600 signs of S₁₂ in 0.19 seconds; exact vectorized 10×10 determinant 15× faster than SJT — the serial n=10 crossover explained and resolved.

Component-isolated benchmarks: ~100× faster than inversion counting, 350–400× faster than merge-based parity, and 15–18× faster than the strongest classical baseline (Narayana stepping with O(1) parity updates). Verified element-by-element through order 10.

Manuscript DA19757 submitted to Discrete Applied Mathematics (Elsevier) as a Note.

New title (“Block Replication and Index Mapping”); strengthened sort-free analysis of meryemPer against naive (suffix sort) and Narayana Pandita (suffix reversal) generators. Zenodo v2.

The Monthly's board judged the work algorithmic rather than pure-mathematical — out of scope for their venue. The feedback redirected berkeDet to algorithms journals, where it belongs.

ORCID profile created (0009-0002-8017-5400); work shared with the community.

Submitted to The American Mathematical Monthly (submission ID 265600446).

detsignper.org launched; video presentation published on YouTube; preprint v1 archived on Zenodo (DOI 10.5281/zenodo.19115506), establishing priority.

The dual iterative algorithm — meryemSign and meryemPer — completed, with the first manuscript and the visual presentation of the meryemPer patterns (orders 2 through 9). The idea itself traces back more than twenty years, to a young student who saw the pattern before knowing its name.