Talk:Factoradic

From Wikipedia, the free encyclopedia

Have received information from Peter Cameron to the effect that he first heard about factoradics from a talk attended in the mid-1980's, when the speaker used the term as if it was already standard. So without a source from that era, the best one can say is the origin is simply obscure. --J. W. McLeod 20:57, 29 Mar 2005 (UTC)

I think the problem may be that this is obvious, and has probably been invented several times. I once described it in Usenet as "factorial base" in January 2002[1], and I did not think it was anything special. Nor can I remember being told about it by anyone else before I used it myself to solve a minor problem. --Henry Bottomley 13:13, 3 Jun 2005 (UTC)

Donald E Knuth's The Art of Computer Programming provides additional information. In Volume 4, Fascicle 2: Generating All Tuples and Permutations the answer to question 7.2.1.2-3 on page 101 cites H. A. Rothe, Sammlung combinatorisch-analytischer Abhandlungen, 2 (1800), 263-264. He refers to inversion tables in question 5.1.1-7, and notes that he described the factorial number system in equation 4.1-(10). It also shows up earlier as the Algorithm P in section 3.3.2 Empirical Tests (for random numbers), pp 65-66 of Volume 2. Knuth also refers to a "Narayana cited in Section 7.2.1.7", which would be the history of combinatorics that is currently being drafted. So factoradics would seem to have been kicking around for over two centuries in one form or the other. --J. W. McLeod 15:05, 4 Jun 2005 (UTC)

---

At first look the last always zero digit in the definition seems redundant, but it's used in the algorithm for making a permutation from factoradic, so either the algorithm should be corrected or the last always zero digit should be present in the definition. Besides it fits nicely because you can just start counting from zero: the factoradic d_n...d₂d₁d₀ is equal to 0!d₀ + 1!d₁ + 2!d₂ + ... + n!d_n, where every digit d_i is in [0, i].

There is a major contradiction on this page, and I don't know how to solve it, so I'm hoping someone else will. At the beginning, and at the first table of numbers, a notation is used such that the nth radix is n!, but after that a notation is used such that the nth radix is (n-1)!. At the beginning 719 would be 54321, but after that it would be 543210. This is EXTREMELY confusing! Someone who actually knows about factoradic, please change this! Soon!

[edit] Non-integers

I was at the 0.999... page and it gave an example that "In the factoradic system, 1 = 1.000… = 0.1234…" . but the current Factoradic article doesn't seem to allow for a 'decimal' point. I would think that either the 0.999... article should have the factoradic example removed or the Factoradic article should be added to. It seems to me like there are different ways to implement a 'decimal' point though, and that having one could make there be multiple representations for the same number (1₁0₀.0₀1₁ would be another way of representing 2, right?) --Sgt. Muffles 18:56, 27 November 2006 (UTC)