Stars and bars (combinatorics): Revision history

23 April 2025

• cur
  Undo
• curprev 22:2322:23, 23 April 2025 197.3.145.222 talk 18,659 bytes 0 →Theorem one proof undo Tag: Reverted

9 April 2025

• Undo
• curprev 07:5007:50, 9 April 2025 206.71.205.238 talk 18,717 bytes +58 No edit summary undo Tags: Reverted Visual edit Mobile edit Mobile web edit

30 March 2025

• Undo
• curprev 19:0119:01, 30 March 2025 42.108.81.233 talk 18,660 bytes 0 →Theorem one undo Tags: Reverted Mobile edit Mobile web edit
• curprev 19:0019:00, 30 March 2025 42.108.81.233 talk 18,660 bytes +1 No edit summary undo Tags: Reverted Mobile edit Mobile web edit

26 February 2025

• WP:JWB) undo

22 February 2025

• curprev 07:0307:03, 22 February 2025 2601:1c2:c000:5de0:cc14:45cd:c7c7:82d0 talk 18,623 bytes +1 Fixed typo. Was 'represetations', now 'representations'. undo Tag: Visual edit

30 January 2025

• curprev 08:0508:05, 30 January 2025 Quiveror talk contribs m 18,622 bytes −10 My bad undo Tags: Manual revert Visual edit Mobile edit Mobile web edit
• curprev 07:5707:57, 30 January 2025 Quiveror talk contribs m 18,632 bytes +10 Typo undo Tags: Reverted Visual edit Mobile edit Mobile web edit
• curprev 07:0907:09, 30 January 2025 Nickalh talk contribs m 18,622 bytes +1 replaced the word "simple" with "a variety of". This is often covered in a 2nd semester university discrete math course, which means many students would not consider it simple. undo

26 December 2024

• Undo
• curprev 16:0416:04, 26 December 2024 2600:1002:b139:9ef3:9444:bdff:fee4:e90d talk 27,897 bytes +4,631 →Theorem one proof: ==Proofs via the method of stars and bars== ===Theorem one proof=== The problem of enumerating ''k''-tuples whose sum is ''n'' is equivalent to the problem of counting configurations of the following kind: let there be ''n'' objects to be placed into ''k'' bins, so that all bins contain at least one object. The bins are distinguished (say they are numbered 1 to ''k'') but the ''n'' objects are not (so configurations are only distinguished by the ''number of objects'' p... undo Tags: Reverted Mobile edit Mobile web edit
• curprev 15:5915:59, 26 December 2024 2600:1002:b139:9ef3:9444:bdff:fee4:e90d talk 23,266 bytes +4,645 →Proofs via the method of stars and bars: ==Proofs via the method of stars and bars== ===Theorem one proof=== The problem of enumerating ''k''-tuples whose sum is ''n'' is equivalent to the problem of counting configurations of the following kind: let there be ''n'' objects to be placed into ''k'' bins, so that all bins contain at least one object. The bins are distinguished (say they are numbered 1 to ''k'') but the ''n'' objects are not (so configurations are only distinguished by the '... undo Tags: Reverted Mobile edit Mobile web edit

10 December 2024

• curprev 15:0715:07, 10 December 2024 Will Orrick talk contribs 18,621 bytes −17 Change indexing of bar positions and of bins to begin with 1, for consistency throughout the article. undo

9 December 2024

• curprev 04:4704:47, 9 December 2024 Will Orrick talk contribs 18,638 bytes +596 Added an example to the introduction so that the main idea can be seen before reading through the theorem statements and discussion of multisets. undo

8 December 2024

• curprev 22:5422:54, 8 December 2024 Will Orrick talk contribs 18,042 bytes +71 No edit summary undo
• curprev 22:5122:51, 8 December 2024 Will Orrick talk contribs 17,971 bytes +650 No edit summary undo
• curprev 16:3816:38, 8 December 2024 Will Orrick talk contribs 17,321 bytes +1,201 Make "Relation between Theorems one and two" its own section. "Examples" --> "Further examples" and make some wording changes. Rm remark about "word problems", which was mislinked. Merge Example 4 into section on generating functions, now at the end, and revise the exposition. Move remark about diagonals of Pascal's triangle to immediately follow Thm two. undo

7 December 2024

• curprev 23:0923:09, 7 December 2024 Will Orrick talk contribs 16,120 bytes −6 →Theorem two proof: Swapped second and third paragraphs of proof to match order in the statement of the theorem. Also, "position" was being used in different ways between the paragraphs, so I rephrased the now third paragraph using "slots" instead of positions. undo
• curprev 04:3204:32, 7 December 2024 Will Orrick talk contribs 16,126 bytes −3 →Theorem two: missing "the"; "cardinality" --> "size" undo
• curprev 04:2604:26, 7 December 2024 Will Orrick talk contribs 16,129 bytes +554 →Example: Extend example to include the multisets of the proof of Theorem two. undo

6 December 2024

• curprev 19:5719:57, 6 December 2024 Will Orrick talk contribs 15,575 bytes +78 →Theorem two: Replace "cardinality" with "size". Condense multiple, redundant lines of displayed equations to one line for clarity and brevity. Provide explanation and link for multiset coefficient. undo
• curprev 19:3919:39, 6 December 2024 Will Orrick talk contribs 15,497 bytes −165 Removed problemetic statement about negative binomial distribution from the introduction. "Problematic" for a number of reasons: not suitable for the the introduction; not clear how it relates to the counting method of this article; "different support ranges" unclear; a theorem is not a coefficient. undo
• curprev 18:1118:11, 6 December 2024 Will Orrick talk contribs 15,662 bytes +56 →Theorem two: Move links to earlier occurrences. Theorem two now states the binomial coefficient formula, for those not familiar with multisets and multichoose. undo
• curprev 17:3317:33, 6 December 2024 Will Orrick talk contribs 15,606 bytes +466 Reorder statements in Theorem two to match what's in the proof. Typo corrections. Elaborate on different multiset interpretations and how this corresponds to interchanging bars and stars. undo
• curprev 17:0717:07, 6 December 2024 Will Orrick talk contribs 15,140 bytes +836 →Proofs via the method of stars and bars: Revised proof of Theorem 2: the theorem statement talks about multisets, so this needed to be addressed in the proof; also added relation to the object-bin model; separated example from proof and sharpened relation between Theorem 1 and Theorem 2 undo
• curprev 16:3116:31, 6 December 2024 Will Orrick talk contribs 14,304 bytes +508 Revised statement and proof of Theorem 1: moved link to combinations article from the proof into the example following the theorem statement; separated the proof from the example; elaborated on the correspondence between the k-tuple problem and the counting problem with objects and bins; other wording changes. undo
• Undo
• curprev 13:1313:13, 6 December 2024 50.100.205.138 talk 13,796 bytes 0 →Theorem two undo Tag: Reverted

4 November 2024

• curprev 00:5900:59, 4 November 2024 Aoa7386 talk contribs m 13,796 bytes −27 No edit summary undo

15 October 2024

• curprev 15:0515:05, 15 October 2024 77.67.113.135 talk 13,823 bytes −10 →Examples undo Tag: Visual edit

16 August 2024

• HG) (3.4.12) undo Tags: Huggle Rollback
• curprev 14:3914:39, 16 August 2024 103.172.240.63 talk 13,873 bytes +13 →Theorem one undo Tag: Reverted
• curprev 14:2914:29, 16 August 2024 103.172.240.63 talk 13,860 bytes −20 →Theorem one undo Tag: Reverted
• curprev 14:2914:29, 16 August 2024 103.172.240.63 talk 13,880 bytes +47 →Theorem one undo Tag: Reverted

31 July 2024

• curprev 09:2309:23, 31 July 2024 218.185.248.66 talk 13,833 bytes +1 Missing period undo

20 June 2024

• curprev 17:2317:23, 20 June 2024 Nichole as a unique name talk contribs 13,832 bytes +164 added a statement that the theorems are used for the coefficients in the negative binomial distribution undo Tags: Visual edit Mobile edit Mobile web edit

16 June 2024

• Report bugs. | Suggested by Headbomb | #UCB_toolbar undo

5 June 2024

• Undo
• curprev 07:4007:40, 5 June 2024 189.219.191.226 talk 13,105 bytes −519 No edit summary undo Tags: Reverted Visual edit Mobile edit Mobile web edit

16 May 2024

• curprev 15:1715:17, 16 May 2024 Will Orrick talk contribs 13,624 bytes +900 →Example 5: include earlier proceedings ref for Ehrenfest and Kamerlingh Onnes paper; elaboration and slight correction on "complexions" with added ref; correction of graphical representation: Ehrenfest and Kamerlingh Onnes did not use a bar undo

15 May 2024

• curprev 21:0121:01, 15 May 2024 Will Orrick talk contribs 12,724 bytes −81 Remove unsourced claim that the method was popularized by Feller. Give the correct year for the 3rd edition of Feller's book. undo

20 April 2024

• curprev 00:0400:04, 20 April 2024 138.51.87.166 talk 12,805 bytes −1 →Theorem two undo Tag: Manual revert
• curprev 00:0200:02, 20 April 2024 138.51.87.166 talk 12,806 bytes +1 →Theorem two undo Tag: Reverted

24 March 2024

• Undo
• curprev 19:3219:32, 24 March 2024 SeverinPappadeux talk contribs m 12,804 bytes +40 →See also: Dirichlet-Multinomial extends stars&stripes for case where x_i could be 0. undo Tag: Visual edit

15 March 2024

• curprev 04:0204:02, 15 March 2024 67.248.244.166 talk 12,764 bytes −1 →Theorem two proof undo Tags: Reverted Visual edit
• curprev 04:0104:01, 15 March 2024 67.248.244.166 talk 12,765 bytes 0 →Theorem two proof: Switched Stars and bars to be consistent with explanation of first theorem and explanation on Combination page. I believe that this is what original/other author(s) indented. undo Tags: Reverted Visual edit