@article {1855,
	title = {A sufficient condition for non-uniqueness in binary tomography with absorption},
	journal = {Theoretical Computer Science},
	volume = {346},
	year = {2005},
	month = {2005},
	pages = {335-357},
	type = {Journal Article},
	abstract = {<p>A new kind of discrete tomography problem is introduced: the reconstruction of discrete sets from their absorbed projections. A special case of this problem is discussed, namely, the uniqueness of the binary matrices with respect to their absorbed row and column sums when the absorption coefficient is n=log((1+5^0.5)/2). It is proved that if a binary matrix contains a special structure of 0s and 1s, called alternatively corner-connected component, then this binary matrix is non-unique with respect to its absorbed row and column sums. Since it has been proved in another paper [A. Kuba, M. Nivat, Reconstruction of discrete sets with absorption, Linear Algebra Appl. 339 (2001) 171194] that this condition is also necessary, the existence of alternatively corner-connected component in a binary matrix gives a characterization of the non-uniqueness in this case of absorbed projections. <tt> </tt></p>},
	doi = {10.1016/j.tcs.2005.08.024},
	author = {Attila Kuba and Maurice Nivat}
}
