Geodesic
On the number of subsets of the residue ring such that the difference of any pair of elements is not invertible
Diskretnaya Matematika, Tome 28 (2016) no. 4, pp. 122-138

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The paper is concerned with subsets $I$ of the residue group ${Z_d}$ in which the difference of any two elements is not relatively prime to $d$. The class of such subsets is denoted by $U\left( d \right)$, the class of sets from $U\left( d \right)$ of cardinality $r$ is denoted by $U\left( {d,\;r} \right)$. The present paper gives formulas for evaluation or estimation of $\left| {U\left( d \right)} \right|$ and $\left| {U\left( {d,\;r} \right)} \right|$.
Keywords: residue ring, nonunit differences, enumerative combinatorics. 
@article{DM_2016_28_4_a9,
     author = {P. V. Roldugin},
     title = {On the number of subsets of the residue ring such that the difference of any pair of elements is not invertible},
     journal = {Diskretnaya Matematika},
     pages = {122--138},
     publisher = {mathdoc},
     volume = {28},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2016_28_4_a9/}
}
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P. V. Roldugin. On the number of subsets of the residue ring such that the difference of any pair of elements is not invertible. Diskretnaya Matematika, Tome 28 (2016) no. 4, pp. 122-138. http://geodesic.mathdoc.fr/item/DM_2016_28_4_a9/