Mathematics desk
< June 9	<< May \| June \| Jul >>	June 11 >

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

June 10[edit]

Combinatorics/set partition(s) relation to the divisibility of natural numbers[edit]

Is there a relation between the divisibility of numbers and combinatorics/set partitions?(Thanks.)--82.137.13.98 (talk) 10:52, 10 June 2017 (UTC)[reply]

See Ramanujan's congruences for number theoretical partitions. For the number of set partitions, aka Bell numbers, OEIS: A000110 lists a few properties. For example, if p is prime then a(p) = 2 (mod p), and more generally a(p^m) ≡ m+1 (mod p). Also a(n) ≠ 0 or 6 (mod 8). --RDBury (talk) 14:40, 10 June 2017 (UTC)[reply]

There is an interesting aspect to be underlined: that of divisibility of expressions involving combinations C(n,k) like the expression (C(2p,p) - 2) when n=2p, k=p, p a prime--82.79.115.105 (talk) 19:56, 16 June 2017 (UTC) number divisible to 2 in this case.--82.79.115.105 (talk) 19:46, 16 June 2017 (UTC)[reply]

From the point of view of mathematics education it is desirable that a natural connection between set theory and number theory be made when the operation of division (especially when the remainder is non-zero) is taught but also when the addition, subtraction and multiplication operations are introduced in elementary mathematics with (semi)concrete models based on set of objects and their cardinalities.--82.79.115.105 (talk) 19:56, 16 June 2017 (UTC)[reply]