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authorChris Wells <chris@mathematicaster.org>2026-05-29 07:26:38 -0500
committerChris Wells <chris@mathematicaster.org>2026-05-29 07:26:38 -0500
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+@article{deleo_discrepancy,
+ title = {A finite victory over de Bruijn&ndash;Erdős in interval discrepancy},
+ author = {DeLeo, Jared and Henderschedt, Owen and Wells, Chris},
+ month = {may},
+ year = {2026},
+ eprint = {2605.29166},
+ eprinttype = {arXiv},
+ eprintclass = {math.CO},
+ archivePrefix = {arXiv},
+ archiveClass = {math.CO},
+ abstract = {We study a finite form of the classical interval discrepancy problem. Starting from the unit interval, one repeatedly splits an existing interval into two until $n$ intervals have been produced. The discrepancy of such a process is the maximum, over all intermediate stages, of the ratio between the longest interval and the shortest interval. A theorem of de Bruijn and Erdős from 1949 shows that this ratio must approach $2$ as $n\to\infty$, and they give a sharp construction achieving this bound. For fixed $n$, their construction gives the upper bound $\operatorname{disc}(n)\leq 2-\frac{3}{2n}+O(1/n^2)$. In this paper, we improve the first-order term of this bound. Specifically, we construct a strategy, called <em>lex-merge</em>, with $\operatorname{disc}(n)\leq 2-\frac{4\ln 2}{n}+O(1/n^2)$. We prove also the lower bound $\operatorname{disc}(n)\geq 2-\frac{6\ln 2}{n}-O(1/n^2)$, showing that the first-order term in this improvement over the de Bruijn&ndash;Erdős construction has the correct order of magnitude. We conjecture that the lex-merge strategy is optimal for every $n$.},
+}
+
@article{briggs_gromov,
title={A discrete view of Gromov's filling area conjecture},
- author={Joseph Briggs and Chris Wells},
+ author={Briggs, Joseph and Wells, Chris},
month = {feb},
year={2026},
eprint={2602.17859},