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Diskr. Mat., 2016, Volume 28, Issue 4, Pages 122–138 (Mi dm1397)  

On the number of subsets of the residue ring such that the difference of any pair of elements is not invertible

P. V. Roldugin

Moscow State Technical University of Radioengineering, Electronics and Automation

Abstract: 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 $U( d )$, the class of sets from $U( d )$ of cardinality $r$ is denoted by $U( {d,\;r} )$. The present paper gives formulas for evaluation or estimation of $| {U( d )} |$ and $| {U( {d,\;r} )} |$.

Keywords: residue ring, nonunit differences, enumerative combinatorics.

DOI: https://doi.org/10.4213/dm1397

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English version:
Discrete Mathematics and Applications, 2018, 28:2, 83–96

Bibliographic databases:

UDC: 519.115
Received: 17.02.2016

Citation: P. V. Roldugin, “On the number of subsets of the residue ring such that the difference of any pair of elements is not invertible”, Diskr. Mat., 28:4 (2016), 122–138; Discrete Math. Appl., 28:2 (2018), 83–96

Citation in format AMSBIB
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