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On certain sets of divisors of a number

✍ Scribed by M. Herzog; J. Schönheim

Publisher
Elsevier Science
Year
1972
Tongue
English
Weight
325 KB
Volume
1
Category
Article
ISSN
0012-365X

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📜 SIMILAR VOLUMES

Extremal theorems on divisors of a numbe
Extremal theorems on divisors of a number
✍ Shuo-Yen Robert Li 📂 Article 📅 1978 🏛 Elsevier Science 🌐 English ⚖ 884 KB

For e-.ery positive integer IV, we determine the rnaxintum sizes of collections C and C' of divisors of N subject to the following restrictions. 1' any IWO numbers in C are coprime. then their least common multiple must he N. If any k nu nbers (k arbitrary) in C' have the greatest common divisor 1.

On the density of sets of divisors
On the density of sets of divisors
✍ R.E.L. Aldred; R.P. Anstee 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 214 KB

Consider the lattice of divisors of n, [1, n]. For any downset (ideal) J in [1, n] we get a forbidden configuration theorem of the type that if a set of divisors D avoids certain configurations, then ] D ] ~< I J ]. If we let 5 ¢ be the set of minimal elements of [ 1, n] not in J, then we forbid in