Maximal sets of integers not containing $k+1$ pairwise coprimes and having divisors from a specified set of primes

Abstract : We find the formula for the cardinality of maximal set of integers from $[1,\ldots,n]$ which does not contain $k+1$ pairwise coprimes and has divisors from a specified set of primes. This formula is defined by the set of multiples of the generating set, which does not depend on $n$.
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Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.335-340, 2005, DMTCS Proceedings
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Vladimir Blinovsky. Maximal sets of integers not containing $k+1$ pairwise coprimes and having divisors from a specified set of primes. Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.335-340, 2005, DMTCS Proceedings. 〈hal-01184442〉

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