简介：Foranyx∈(0,1](exceptatmostcountablymanypoints),thereexistsauniquesequence{dn(x)}n≥1ofintegers,calledthedigitsequenceofx,suchthat■.ThedexterinfiniteseriesexpansioniscalledtheL¨urothexpansionofx.ThispaperisconcernedwiththesizeofthesetofpointsxwhosedigitsequenceinitsL¨urothexpansionisstrictlyincreasingandcontainsarbitrarilylongarithmeticprogressionswitharbitrarycommondifference.Moreprecisely,wedeterminetheHausdorffdimensionoftheaboveset.
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