TY - JOUR
T1 - Induced arithmetic removal
T2 - complexity 1 patterns over finite fields
AU - Fox, Jacob
AU - Tidor, Jonathan
AU - Zhao, Yufei
N1 - Publisher Copyright:
© 2022, The Hebrew University of Jerusalem.
PY - 2022/5
Y1 - 2022/5
N2 - We prove an arithmetic analog of the induced graph removal lemma for complexity 1 patterns over finite fields. Informally speaking, we show that given a fixed collection of r-colored complexity 1 arithmetic patterns over Fq, every coloring ϕ:Fqn\{0}→[r] with o(1) density of every such pattern can be recolored on an o(1)-fraction of the space so that no such pattern remains.
AB - We prove an arithmetic analog of the induced graph removal lemma for complexity 1 patterns over finite fields. Informally speaking, we show that given a fixed collection of r-colored complexity 1 arithmetic patterns over Fq, every coloring ϕ:Fqn\{0}→[r] with o(1) density of every such pattern can be recolored on an o(1)-fraction of the space so that no such pattern remains.
UR - https://www.scopus.com/pages/publications/85125778851
UR - https://www.scopus.com/inward/citedby.url?scp=85125778851&partnerID=8YFLogxK
U2 - 10.1007/s11856-022-2290-x
DO - 10.1007/s11856-022-2290-x
M3 - Article
AN - SCOPUS:85125778851
SN - 0021-2172
VL - 248
SP - 1
EP - 38
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -