15:{"metadata":[["$","title","0",{"children":"En Tres Juegos con Diámetro No Decreciente"}],["$","meta","1",{"name":"description","content":"Vamos a $[a,b]$ denotar los números enteros entre $a$ y $b$ inclusiva y, para un subconjunto finito $X \\subseteq \\mathbb{Z}$, dejar que el diámetro de $X$ ser igual a $\\max(X)-\\min(X)$. Escribimos X X<_p\\, Y provided proporcionado provided \\ max (X)< \\ min(Y) Y. Para un entero positivo $m$, deje que $f(m,m,m;2)$ ser el menor entero $N$ que cualquier $2$-colorear $\\Delta: [1, N]\\rightarrow \\{0,1\\}$ tiene tres monocromática $m$-establece $B_1, B_2, B_3 \\subseteq [1,N]$ (no necesariamente del mismo color) con $B_1<_p\\, B_2 <_p\\, B_3$ y $diam(B_1)\\leq diam(B_2)\\leq diam(B_3)$. La mejora en los límites superior e inferior de Bialostocki, Erd\\H os y Lefmann, nos muestran que $f(m,m,m;2)=8m-5 \\lfloor\\frac{2m-2}{3}\\rfloor \\delta$ para $m\\geq 2$, donde $\\delta=1$ si $m\\in \\{2,5\\}$ y $\\delta=0$ lo contrario."}],["$","meta","2",{"name":"author","content":"Daniel Bernstein"}],["$","meta","3",{"name":"author","content":"David J. Grynkiewicz"}],["$","meta","4",{"name":"author","content":"Carl R. Yerger"}],["$","meta","5",{"name":"keywords","content":"Combinatorics"}],["$","meta","6",{"name":"referrer","content":"origin"}],["$","meta","7",{"name":"robots","content":"index, follow"}],["$","link","8",{"rel":"canonical","href":"https://synthical.com/article/En-Tres-Juegos-con-Di%C3%A1metro-No-Decreciente-1b65a984-43bc-4147-bb3c-60a80da89ab1"}],["$","link","9",{"rel":"alternate","hrefLang":"de-DE","href":"https://synthical.com/article/En-Tres-Juegos-con-Di%C3%A1metro-No-Decreciente-1b65a984-43bc-4147-bb3c-60a80da89ab1/de"}],["$","link","10",{"rel":"alternate","hrefLang":"fr-FR","href":"https://synthical.com/article/En-Tres-Juegos-con-Di%C3%A1metro-No-Decreciente-1b65a984-43bc-4147-bb3c-60a80da89ab1/fr"}],["$","link","11",{"rel":"alternate","hrefLang":"es-ES","href":"https://synthical.com/article/En-Tres-Juegos-con-Di%C3%A1metro-No-Decreciente-1b65a984-43bc-4147-bb3c-60a80da89ab1/es"}],["$","link","12",{"rel":"alternate","hrefLang":"it-IT","href":"https://synthical.com/article/En-Tres-Juegos-con-Di%C3%A1metro-No-Decreciente-1b65a984-43bc-4147-bb3c-60a80da89ab1/it"}],["$","link","13",{"rel":"alternate","hrefLang":"ru-RU","href":"https://synthical.com/article/En-Tres-Juegos-con-Di%C3%A1metro-No-Decreciente-1b65a984-43bc-4147-bb3c-60a80da89ab1/ru"}],["$","meta","14",{"property":"og:title","content":"En Tres Juegos con Diámetro No Decreciente"}],["$","meta","15",{"property":"og:description","content":"Vamos a $[a,b]$ denotar los números enteros entre $a$ y $b$ inclusiva y, para un subconjunto finito $X \\subseteq \\mathbb{Z}$, dejar que el diámetro de $X$ ser igual a $\\max(X)-\\min(X)$. Escribimos X X<_p\\, Y provided proporcionado provided \\ max (X)< \\ min(Y) Y. Para un entero positivo $m$, deje que $f(m,m,m;2)$ ser el menor entero $N$ que cualquier $2$-colorear $\\Delta: [1, N]\\rightarrow \\{0,1\\}$ tiene tres monocromática $m$-establece $B_1, B_2, B_3 \\subseteq [1,N]$ (no necesariamente del mismo color) con $B_1<_p\\, B_2 <_p\\, B_3$ y $diam(B_1)\\leq diam(B_2)\\leq diam(B_3)$. La mejora en los límites superior e inferior de Bialostocki, Erd\\H os y Lefmann, nos muestran que $f(m,m,m;2)=8m-5 \\lfloor\\frac{2m-2}{3}\\rfloor \\delta$ para $m\\geq 2$, donde $\\delta=1$ si $m\\in \\{2,5\\}$ y $\\delta=0$ lo contrario."}],["$","meta","16",{"property":"og:url","content":"https://synthical.com/article/En-Tres-Juegos-con-Di%C3%A1metro-No-Decreciente-1b65a984-43bc-4147-bb3c-60a80da89ab1/es"}],["$","meta","17",{"property":"og:site_name","content":"Synthical"}],["$","meta","18",{"property":"og:locale","content":"es"}],["$","meta","19",{"property":"og:image","content":"https://synthical.com/preview/article/1b65a984-43bc-4147-bb3c-60a80da89ab1/es"}],["$","meta","20",{"property":"og:image:alt","content":"En Tres Juegos con Diámetro No Decreciente"}],["$","meta","21",{"property":"og:image:width","content":"1200"}],["$","meta","22",{"property":"og:image:height","content":"630"}],["$","meta","23",{"property":"og:type","content":"article"}],["$","meta","24",{"property":"article:published_time","content":"2014-07-18T21:38:58.000Z"}],["$","meta","25",{"property":"article:modified_time","content":"2014-07-18T21:38:58.000Z"}],["$","meta","26",{"property":"article:author:name","content":"Daniel Bernstein"}],["$","meta","27",{"property":"article:author:name","content":"David J. Grynkiewicz"}],["$","meta","28",{"property":"article:author:id","content":"f722aad2-7e52-4ec1-8499-e6093e55dda5"}],["$","meta","29",{"property":"article:author:alternatives","content":"David J. Grynkiewicz"}],["$","meta","30",{"property":"article:author:avatar","content":"default_8"}],["$","meta","31",{"property":"article:author:articles_count","content":"32"}],["$","meta","32",{"property":"article:author:name","content":"Carl R. Yerger"}],["$","meta","33",{"property":"article:author:id","content":"99c85eee-fb75-4725-a2ea-10b0c1c32a5a"}],["$","meta","34",{"property":"article:author:alternatives","content":"Carl R. Yerger"}],["$","meta","35",{"property":"article:author:avatar","content":"default_3"}],["$","meta","36",{"property":"article:author:articles_count","content":"6"}],["$","meta","37",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","38",{"name":"twitter:title","content":"En Tres Juegos con Diámetro No Decreciente"}],["$","meta","39",{"name":"twitter:description","content":"Vamos a $[a,b]$ denotar los números enteros entre $a$ y $b$ inclusiva y, para un subconjunto finito $X \\subseteq \\mathbb{Z}$, dejar que el diámetro de $X$ ser igual a $\\max(X)-\\min(X)$. Escribimos X X<_p\\, Y provided proporcionado provided \\ max (X)< \\ min(Y) Y. Para un entero positivo $m$, deje que $f(m,m,m;2)$ ser el menor entero $N$ que cualquier $2$-colorear $\\Delta: [1, N]\\rightarrow \\{0,1\\}$ tiene tres monocromática $m$-establece $B_1, B_2, B_3 \\subseteq [1,N]$ (no necesariamente del mismo color) con $B_1<_p\\, B_2 <_p\\, B_3$ y $diam(B_1)\\leq diam(B_2)\\leq diam(B_3)$. La mejora en los límites superior e inferior de Bialostocki, Erd\\H os y Lefmann, nos muestran que $f(m,m,m;2)=8m-5 \\lfloor\\frac{2m-2}{3}\\rfloor \\delta$ para $m\\geq 2$, donde $\\delta=1$ si $m\\in \\{2,5\\}$ y $\\delta=0$ lo contrario."}],["$","meta","40",{"name":"twitter:image","content":"https://synthical.com/preview/article/1b65a984-43bc-4147-bb3c-60a80da89ab1/es"}],["$","meta","41",{"name":"twitter:image:alt","content":"En Tres Juegos con Diámetro No Decreciente"}],["$","meta","42",{"name":"twitter:image:width","content":"1200"}],["$","meta","43",{"name":"twitter:image:height","content":"630"}],["$","link","44",{"rel":"icon","href":"/favicon-32x32.png"}],["$","link","45",{"rel":"apple-touch-icon","href":"/apple-touch-icon.png"}]],"error":null,"digest":"$undefined"}