2012/07/17 by Hajdu, Lajos, Tijdeman, Rob
#15A06 #94A08 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1207.3933
In earlier papers we have developed an algebraic theory of discrete tomography. In those papers the structure of the functions f: A → \0,1\ and f: A → ℤ having given line sums in certain directions have been analyzed. Here A was a block in ℤn with sides parallel to the axes. In the present paper we assume that there is noise in the measurements and (only) that A is an arbitrary or convex finite set in ℤn. We derive generalizations of earlier results. Furthermore we apply a method of Beck and Fiala to obtain results of he following type: if the line sums in k directions of a function h: A → [0,1] are known, then there exists a function f: A → \0,1\ such that its line sums differ by at most k from the corresponding line sums of h.