Peirce Numbers
Jon Awbrey
jawbrey at oakland.edu
Tue Mar 12 02:47:03 CET 2002
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no, sorry, the array here looks like:
| 1
| 2 1
| 5 3 2
| 15 10 7 5
| 52 37 27 20 15
| 203 151 114 87 67 52
but i seem to remember this somewhere?
martin gardner's 1978 article on bell's
might have mentioned peirce, but now
i'm just guessing ...
jon awbrey
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Jon Awbrey wrote:
>
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> | Charles Sanders Peirce, "On the Algebra of Logic",
> |'American Journal of Mathematics, Vol. 3, pages 15-57, 1880.
> |
> | appears as CP 3.154-251, pages 104-157, in:
> |
> |'Collected Papers of Charles Sanders Peirce',
> | Volumes 1-6 edited by Charles Hartshorne & Paul Weiss, 1931-35,
> | Volumes 7-8 edited by Arthur W. Burks, 1958,
> | Harvard University Press, Cambridge, MA.
> |
> | appears as CE 4, pages 163-209, in:
> |
> |'Writings of Charles S. Peirce: A Chronological Edition',
> |'Volume 4, 1879-1884', Peirce Edition Project,
> | Indiana University Press, Bloomington, IN, 1986.
>
> Enumerates "the number of individual forms for the (n+2)-fold relative",
> with Taylor series expansion, finite diff formula, and generating array,
> at (CP 3.229) and (CE 4, 199-200).
>
> Peirce Resources:
>
> Online:
>
> http://members.door.net/arisbe/menu/library/bycsp/bycsp.htm
>
> CD Format:
>
> http://www.nlx.com/titles/titlpeir.htm
>
> A 'Chronological Edition' of Peirce's Writings
> is being ground out at an agonizingly slow pace:
>
> | Charles Sanders Peirce,
> |'Writings of Charles S. Peirce: A Chronological Edition',
> |'Volume 1: 1857-1866',
> |'Volume 2: 1867-1871',
> |'Volume 3: 1872-1878',
> |'Volume 4: 1879-1884',
> |'Volume 5: 1884-1886',
> |'Volume 6: 18861890',
> | and still counting ...
> | 30-50 volumes expected!
> |
> | Peirce Edition Project,
> | Indiana University Press, Bloomington, IN, 1982-????
> |
> | http://www.iupui.edu/~peirce/web/index.htm
> | http://www.iupui.edu/~peirce/web/desc/desc.htm
> | http://www.iupui.edu/~peirce/web/writings/crit.htm
>
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> Richard Guy wrote:
> >
> > Can anyone give any refs to the following,
> > whose rows add to Bell_(n+2)
> >
> > 2 2 0 0 0 0 0 0 0 0
> > 5 2 3 0 0 0 0 0 0 0
> > 15 2 9 4 0 0 0 0 0 0
> > 52 2 21 24 5 0 0 0 0 0
> > 203 2 45 100 50 6 0 0 0 0
> > 877 2 93 360 325 90 7 0 0 0
> > 4140 2 189 1204 1750 840 147 8 0 0
> > 21147 2 381 3864 8505 6300 1862 224 9 0
> > 115975 2 765 12100 38850 41706 18522 3696 324 10
> >
> > You can get them by multiplying the corresp
> > Stirling numbers of the 2nd kind by k+2.
> >
> > The diagonal 2 9 24 50 90 147 224 324 450 605
> > is A006002 in OEIS, but I didn't find lower
> > diagonals or columns. R.
>
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