Geodesic
Lower and upper bounds for the affinity order of transformations of Boolean vector spaces
Prikladnaâ diskretnaâ matematika, no. 2 (2013), pp. 14-18

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Let $\Phi_n$ be the set of all transformations of the Boolean vector space $V_n$. Affinity order of a mapping $F\in\Phi_n$ is the least order of the set $V_n$ partition with the property: for every its block there exists an affine mapping $A\colon V_n\to V_n$ being equivalent to $F$ on this block. Affinity order of $\Phi_n$ is the greatest order of $F\in\Phi_n$. Upper and lower bounds for the affinity order of $\Phi_n$ are given in the article. These results can be used for estimating complexity of some techniques in Boolean equations resolving.
Keywords: transformation of Boolean vector space, affine mapping, solution complexity of Boolean equations. 
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     author = {S. P. Gorshkov and A. V. Dvinyaninov},
     title = {Lower and upper bounds for the affinity order of transformations of {Boolean} vector spaces},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {14--18},
     publisher = {mathdoc},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2013_2_a1/}
}
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S. P. Gorshkov; A. V. Dvinyaninov. Lower and upper bounds for the affinity order of transformations of Boolean vector spaces. Prikladnaâ diskretnaâ matematika, no. 2 (2013), pp. 14-18. http://geodesic.mathdoc.fr/item/PDM_2013_2_a1/