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- W2896773761 abstract "Let $mathcal{D}_0:= {x + iy vert x, y >0}$, and let $(L, R)$ be a pair of M{o}bius transformations corresponding to $mathrm{SL}_2(mathbb{N}_0)$ matrices such that $R(mathcal{D}_0)$ and $L(mathcal{D}_0)$ are disjoint. Given such a pair (called a left-right pair), we can construct a directed graph $mathcal{F}(L, R)$ with vertices $mathcal{D}_0$ and edges ${(z, R(z))}_{z in mathcal{D}_0} cup {(z, L(z))}_{z in mathcal{D}_0}$, which is a collection of infinite binary trees. We answer two questions of Nathanson by classifying all the pairs of elements of $mathrm{SL}_2(mathbb{N}_0)$ whose corresponding M{o}bius transformations form left-right pairs and showing that trees in $mathcal{F}(L, R)$ are always rooted." @default.
- W2896773761 created "2018-10-26" @default.
- W2896773761 creator A5087889635 @default.
- W2896773761 date "2018-10-10" @default.
- W2896773761 modified "2023-09-27" @default.
- W2896773761 title "Left-Right Pairs and Complex Forests of Infinite Rooted Binary Trees" @default.
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