Vol. 9, No. 5, 2016

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
On polynomial configurations in fractal sets

Kevin Henriot, Izabella Łaba and Malabika Pramanik

Vol. 9 (2016), No. 5, 1153–1184
Abstract

We show that subsets of n of large enough Hausdorff and Fourier dimension contain polynomial patterns of the form

(x,x + A1y,,x + Ak1y,x + Aky + Q(y)en),x n,y m,

where Ai are real n × m matrices, Q is a real polynomial in m variables and en = (0,,0,1).

Keywords
configurations in fractals, additive combinatorics
Mathematical Subject Classification 2010
Primary: 11B30
Secondary: 28A80
Milestones
Received: 25 November 2015
Revised: 29 March 2016
Accepted: 29 April 2016
Published: 29 July 2016
Authors
Kevin Henriot
Department of Mathematics
University of British Columbia
1984 Mathematics Road
Vancouver BC V6T 1Z2
Canada
Izabella Łaba
Department of Mathematics
University of British Columbia
1984 Mathematics Road
Vancouver BC V6T 1Z2
Canada
Malabika Pramanik
Department of Mathematics
University of British Columbia
1984 Mathematics Road
Vancouver BC V6T 1Z2
Canada