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New research quantifies imbalance in Latin rectangles

By PulseAugur Editorial · [1 sources] ·

This paper explores the concept of balance in Latin rectangles, viewing them as points in a grid and measuring their imbalance using the L1 metric. Researchers developed a simulated annealing approach that improves upon existing benchmarks for non-square rectangles and provides a computer-assisted proof for the optimality of a previously found minimum imbalance value. The study also establishes asymptotic bounds for the minimum imbalance and investigates the conditions for perfect balance, with all reported rectangles verified using the Lean 4 programming language and its Mathlib library. AI

RANK_REASON The cluster contains an academic paper detailing new mathematical research. [lever_c_demoted from research: ic=1 ai=0.1]

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New research quantifies imbalance in Latin rectangles

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The cluster contains an academic paper detailing new mathematical research. [lever_c_demoted from research: ic=1 ai=0.1]
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COVERAGE [1]

  1. arXiv cs.AI TIER_1 English(EN) · Zhengyu Li, Vijay Ganesh ·

    How Unbalanced Must a Latin Rectangle Be?

    arXiv:2611.06003v1 Announce Type: cross Abstract: We view a $k\times n$ Latin rectangle as $n$ points in the grid $[n]^k$. Each symbol gives one point, whose coordinates are the columns it occupies. The rectangle is balanced when these points are pairwise equidistant in the $\ell…

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