is a tiny wandering imaginary dinosaur which migrated from AOL in October of 2008.

Thinking Lizard

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Rhodingeedaddee is my node blog. See my other blogs and recent posts.


[6-16-2009 Update Insert: Most of what is in this space is now moot. I found out what I was doing wrong and have reinstated Archives and Labels searches. They do work. However, in certain cases you may prefer Labels to Archives. Example: 1976 Today begins in November of 2006 and concludes in December of 2006, but there are other related posts in other months. Note: Labels only shows 20 posts at a time. There are 21 hubs, making 21 (which is for 1976 Today) an older hub.] ********************************* to my online poems and song lyrics using Archives. Use hubs for finding archival locations but do not link through them. Originally an AOL Journal, where the archive system was nothing like the system here, this blog was migrated from there to here in October of 2008. Today (Memorial/Veteran's Day, May 25, 2009) I discovered a glitch when trying to use a Blogger archive. Now, it may be template-related, but I am unable to return to S M or to the dashboard once I am in the Archives. Therefore, I've decided on this approach: a month-by-month post guide. The sw you see in the codes here stood for Salchert's Weblog when I began it in November of 2006. It later became Sprintedon Hollow. AOL provided what were called entry numbers, but they weren't consistent, and they didn't begin at the first cardinal number. That is why the numbers after "sw" came to be part of a post's code. ************** Here then is the month-by-month post guide: *2006* November: 00001 through 00046 - December: 00047 through 00056 -- *2007* January: 00057 through 00137 - February: 00138 through 00241 - March: 00242 through 00295 - April: 00296 through 00356 - May: 00357 through 00437 - June: 00438 through 00527 - July: 00528 though 00550 - August: 00551 through 00610 - September: 00611 through 00625 - October: 00626 through 00657 - November: 00658 through 00729 - December: 00730 through 00762 -- *2008* January: 00763 through 00791 - February: 00792 through 00826 - March: 00827 through 00849 - April: 00850 through 00872 - May: 00873 through 00907 - June: 00908 through 00931 - July: 00932 through 00955 - August: 00956 through 00993 - September 00994 through 01005 - October: 01006 through 01007 - November: 01008 through 01011 - December: 01012 through 01014 -- *2009* January: 01015 through 01021 - February: 01022 through 01028 - March: 01029 through 01033 - April: 01034 through 01036 - May: 01037 through 01044 - ******************************************************* 1976 Today: 2006/11 and 2006/12 -- Rooted Sky 2007: 2007/01/00063rsc -- Postures 2007: 2007/01/sw00137pc -- Sets: 2007/02/sw00215sgc -- Venturings: 2007/03/00216vc -- The Undulant Trees: 2007/03/00266utc -- This Day's Poem: 2007/03/00267tdpc -- Autobio: 2007/04/sw00316ac -- Fond du Lac: 2007/04/00339fdl -- Justan Tamarind: 2007/05/sw00366jtc -- Prayers in December: 2007/05/sw00393pindc -- June 2007: 2007/06/sw00440junec -- Seminary: 2007/07/sw00533semc -- Scatterings: 2008/08/00958sc ** Song Lyrics: 2008/02/sw00797slc ********** 2009-06-02: Have set S M to show 200 posts per page. Unfortunately, you will need to scroll to nearly the bottom of a page to get to the next older/newer page.


Saturday, July 28, 2007


09.11.06 Stirling Numbers and Binomial Coefficients Yesterday, in the midst of searching for something else, I found the manilla folder in which I am keeping short mathematical papers I have written. Among these is one wherein I show a way of determining binominal coefficients which is different from the way in general use. I wrote it during the heat of my studying for the GRE. The date on it is September 17, 1983. Alas, my way, while it does work, is merely of some interest, and is not a viable competitor. Nonetheless, being pleased with it, I sent it to a most cordial excellent mathematician in Canada. In his 83:12:07 letter to me/ he* wrote: "Your method for calculating binomial coefficients is more complicated than more usual ways of doing so, but there is some interest, because you have re- discovered the Stirling numbers of the first kind, which crop up all over the place in combinatorial analysis." He also sent a separate sheet to me on which he uses Pascal's Triangle to show me how the Stirling numbers of the first kind operate. To this he provided further explanatory information. I had mentioned Pascal's Triangle in my brief paper, but I did not use it. # Today I went online to learn more about Stirling numbers. I visited two sites. At site one, after going back & forth several times from the triangle depiction of the Stirling numbers of the first kind to the one of the second kind, I suddenly noticed that the natural number summation sequence is integral to both kinds, with the important distinctions that each nnss term in the Stirling numbers of the first kind is preceded by a minus sign, and that the generated terms therein both alternate from negative to positive to negative to positive values and increase in value far more rapidly than do the totally positive terms in the Stirling numbers of the second kind. At site two I found what I always crave: clear examples. The examples presented there illustrate combinations. # Even though my paper does not "merit publication", I've decided to publish it. See entry beneath this one: sw00546math # # Notes: 1. James Stirling was an 18th Century Scottish mathematician. 2. The two triangles showing Stirling numbers of the first kind and Stirling numbers of the second kind are located at: Stirling number 3. The clear combinations examples are at: Brian A. J. Salchert

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