Binaries - Open Access .click

International Journal of Algebra and Computation, 1991
We strengthen the description of the 2-avoidable binary patterns given in J. Cassaigne [3], P. Roth [7], and Vanicek [8], by showing that every 2-avoidable binary pattern [t] can be avoided by an infinite independent set of binary words, and, the number of binary words avoiding [t] grows exponentially with their length.
Pavel Goralcik, Tomas Vanicek
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A binary wavelet decomposition of binary images

IEEE Transactions on Image Processing, 1996
We construct a theory of binary wavelet decompositions of finite binary images. The new binary wavelet transform uses simple module-2 operations. It shares many of the important characteristics of the real wavelet transform. In particular, it yields an output similar to the thresholded output of a real wavelet transform operating on the underlying ...
Mitchell D. Swanson, Ahmed H. Tewfik
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Binary Nontiles

SIAM Journal on Discrete Mathematics, 2012
A subset $V \subseteq \mathbb{F}_2^n$ is a tile if $\mathbb{F}_2^n$ can be covered by disjoint translates of $V$. In other words, $V$ is a tile if and only if there is a subset $A \subseteq \mathbb{F}_2^n$ such that $V+A = \mathbb{F}_2^n$ uniquely (i.e., $v + a = v' + a'$ implies that $v=v'$ and $a=a'$, where $v,v' \in V$ and $a,a' \in A$).
Don Coppersmith, Victor S. Miller
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