Talk:Bell number

message: I've added a section on calculating Bell numbers that doesn't use any equations; I think pictures like this are more accessible than descriptions which use a lot of equations (people have also complained about the typeface we use for math; see, for example, the discussion over at JPEG). Samboy 04:38, 16 May 2005 (UTC)
replies: text: I've put the algorithm after the "theoretical" material; it seems of lesser interest. Michael Hardy 21:03, 16 May 2005 (UTC)
replies: text: One of my goals when making those additions is to present Bell numbers so that an intelligent elementry school kid can understand and even calculate them.  Of course, what I really need to do is add a picture showing the Bell number combining three numbers together (or even have pictures of labelled balls in boxes).  I've added some section headers so that people can go from section to section quickly; this hopefully makes the article more readable.  Samboy 01:11, 17 May 2005 (UTC)
thread_title: Untitled

message: Surely there can be no partitions of an empty set.
If we permit {} to be a partition of {}, then there are an infinite number of partitions of {X}: { {X} }, { {X}, {} }, { {X}, {}, {} } and so on.
The situation is ananlagous to the reason why we do not count 1 as a prime number, because if we did then there would be more than one way to break any number up into prime factors. Indeed, the factorisations of any number are prescisely the ways of dividing up it's set of prime factors into partitions. —The preceding unsigned comment was added by 203.10.224.60 (talk • contribs).
::: A member of a partition cannot be empty.  (No member of the empty set is non-empty!) Michael Hardy (talk) 05:06, 15 August 2010 (UTC)
replies: text: Reliable sources define B0 = 1, so we do the same. It makes good sense to me. The single partition of {} is {} as you correctly write. Your then-part apparently makes the incorrect assumption that the partition is {{}}. A partition is a set of subsets, and the partition of the empty set is the empty set (which means it contains no subsets). The partition does not contain the empty set, and no partition is allowed to contain the empy set. Does this make sense to you? PrimeHunter 10:35, 24 July 2007 (UTC)
replies: text: There are a number of sources that do use or analyse the sequence with B0 = 0.  Ramanujan, for instance, studied it as the 2nd iteration of: a(0) = x; a(n) = e^(a(n-1)) - 1.  This has the advantage that the summations all deal with no constant terms, so standard formula apply on their exponents that have the standard combinatorial interpretations.  That's probably why the combinatorial value of zero works out.  See Berndt's Book 1 of Ramanujan's Notebooks, chapter 4. Ex0du5 5u+u7e (talk) 04:26, 15 August 2010 (UTC)
thread_title:  Empty set 

message: There's a connection with 52 of the 54 symbols used to indicate chapters of the Tale of Genji -- see http://www.viewingjapaneseprints.net/texts/topictexts/artist_varia_topics/genjimon7.html etc.  I believe this is discussed in one of the old Martin Gardner columns.  What we have on Wikipedia now is Japanese incense#Kōdō... -- AnonMoos (talk) 10:02, 20 October 2010 (UTC)
replies: text: On that page, the symbols for chapter 35 and 42 are equivalent, and the symbol for chapter 54 is a strange variant of that for chapter 53, but the remaining 52 symbols illustrate how the number of groupings of five elements is the Bell number 52... AnonMoos (talk) 05:04, 22 October 2010 (UTC)
thread_title: Tale of Genji connection

message: I offer another Python implementation that is a little simpler than the current one
def comb(n, k):
  if k == 0: return 1
  if n == 0: return 0
  e = n - k
  i = n - 1
  c = n
  while i > e:
    c = c*i
    i = i - 1  
  r = (c / factorial(k))
  return r
  
def bell(n):
  if n < 2: return 1
  b = [None]*(n+1)
  b[0] = 1
  b[1] = 1
  for i in range(2, n+1):
    sum_b = 0
    for k in range(i):
      sum_b = sum_b + (b[k]* comb(i-1,k))
    b[i] = sum_b
  return b[n]
If you think it useful, please move it to the main page.  — Preceding unsigned comment added by 24.6.172.74 (talk) 00:46, 4 September 2011 (UTC)
thread_title:  Another Python implementation 

message: Is it just me or does the introduction seem mildly passive aggressive about the name coming from Bell, despite the much older history of the numbers? I might also be completely misreading it.
LudwikSzymonJaniuk (talk) 21:01, 3 November 2019 (UTC)
replies: text: You think it would be an improvement to leave out the word "but"? To remove some of this information from the lead? Or maybe to link to Stigler's law of eponymy to clarify that this kind of misnomer happens all the time? —David Eppstein (talk) 21:25, 3 November 2019 (UTC)
replies: text:  Maybe reversing the two phrases?  "Bell numbers are named after Eric Temple Bell, who wrote about them in the 1930s, although they have been studied by mathematicians since the 19th century, and their roots go back to medieval Japan."  But removing "but" (and splitting the second sentence into 2) also works well.  --JBL (talk) 22:09, 3 November 2019 (UTC)
replies: text: The introduction seems nicely written to me as it is now. In any case, it would be very interesting to know how and when the name "Bell" was attached to this sequence. My guess is that this is relatively recent, and that originated after Martin Gardner's nice divulgative articles about 50 years ago, where he refers to E.T.Bell and his 1930s papers.pma 22:24, 10 January 2020 (UTC)
replies: text: The history of that name is at the end of the article. According to our source (after correcting the date in the source) it's from a paper published 30 years earlier than Gardner. —David Eppstein (talk) 07:20, 11 January 2020 (UTC)
thread_title: Passive aggressive introduction