diff options
| -rw-r--r-- | data/papers.bib | 2 | ||||
| -rw-r--r-- | flake.lock | 32 | ||||
| -rw-r--r-- | flake.nix | 2 |
3 files changed, 18 insertions, 18 deletions
diff --git a/data/papers.bib b/data/papers.bib index fb9ae90..f9bde4b 100644 --- a/data/papers.bib +++ b/data/papers.bib @@ -19,7 +19,7 @@ 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–Erdős construction has the correct order of magnitude. We conjecture that the lex-merge strategy is optimal for every $n$.}, + 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 $\operatorname{disc}(n)\leq 2-\frac{3}{2n}+O\bigl({1\over n^2}\bigr)$. In this paper, we prove that $\operatorname{disc}(n)=2^{1-1/\lceil n/2\rceil}=2-{4\ln 2\over n}+O\bigl({1\over n^2}\bigr)$ for every $n$.} } @article{briggs_gromov, @@ -5,11 +5,11 @@ "nixpkgs-lib": "nixpkgs-lib" }, "locked": { - "lastModified": 1778716662, - "narHash": "sha256-m1Yf0wZ8j1OHjTc2UwHwyQRSnNeSgLJOd7q5Y45hzi4=", + "lastModified": 1788450739, + "narHash": "sha256-glZLQlzIn1fXH6PazR2iUmTo7kzzyYSshrWhLS9TqCU=", "owner": "hercules-ci", "repo": "flake-parts", - "rev": "f7c1a2d347e4c52d5fb8d10cb4d94b5884e546fb", + "rev": "31729ca8cbdb4fa927b34e5f4353e6a83f39e993", "type": "github" }, "original": { @@ -35,11 +35,11 @@ }, "nix-filter_2": { "locked": { - "lastModified": 1730207686, - "narHash": "sha256-SCHiL+1f7q9TAnxpasriP6fMarWE5H43t25F5/9e28I=", + "lastModified": 1757882181, + "narHash": "sha256-+cCxYIh2UNalTz364p+QYmWHs0P+6wDhiWR4jDIKQIU=", "owner": "numtide", "repo": "nix-filter", - "rev": "776e68c1d014c3adde193a18db9d738458cd2ba4", + "rev": "59c44d1909c72441144b93cf0f054be7fe764de5", "type": "github" }, "original": { @@ -50,11 +50,11 @@ }, "nixpkgs": { "locked": { - "lastModified": 1782911522, - "narHash": "sha256-ucCmt+bn4JGfGitaFgiQMHPfODqMIZ9nbHKDVHIRL7w=", + "lastModified": 1790687781, + "narHash": "sha256-/pNu7+ay1nb87v6FlT5jFQlw6Wfov3k78qll4ajPUmc=", "owner": "nixos", "repo": "nixpkgs", - "rev": "a1a6f0fe5442349fc15b6eb956b25d4b2fc21619", + "rev": "99358e9409a4d8ed0a08328b22316a3681814906", "type": "github" }, "original": { @@ -65,11 +65,11 @@ }, "nixpkgs-lib": { "locked": { - "lastModified": 1777168982, - "narHash": "sha256-GOkGPcboWE9BmGCRMLX3worL4EMnsnG8MyKmXNeYuhQ=", + "lastModified": 1788057806, + "narHash": "sha256-DTQSMxzDWmT0zhguthvegnVkn7CFqGCv4IHCzk5ZUpM=", "owner": "nix-community", "repo": "nixpkgs.lib", - "rev": "f5901329dade4a6ea039af1433fb087bd9c1fe14", + "rev": "596e2e3940e09b2abbeb03f75fa1828c57fcd72c", "type": "github" }, "original": { @@ -129,11 +129,11 @@ "systems": "systems_2" }, "locked": { - "lastModified": 1770582573, - "narHash": "sha256-dmFQ5Wis0XZznnvARSX7kHt+GFl7X9KTWSVchQ8MK1c=", + "lastModified": 1784291704, + "narHash": "sha256-GOVjf8+dqf7bU3E+LvKhqRFrMaptNtLIXkncGCIrj3A=", "ref": "refs/heads/master", - "rev": "f3ab054aef8cce1fc2b56fec48a20e1764e017a1", - "revCount": 9, + "rev": "fbe2ae6f3241f4b289590cd64fea5a935aeca85d", + "revCount": 10, "type": "git", "url": "git://git.mathematicaster.org/www/assets.git" }, @@ -85,7 +85,7 @@ # site = config.packages.www-main; site = pkgs.haskellPackages.www-main; texPath = [ - pkgs.texlive.combined.scheme-full + pkgs.texliveFull ]; }; site = pkgs.runCommandLocal "build-site" {} '' |