The Number of Two-Terminal Series-Parallel Networks. John Riodan, C. E. Shannon, Claude Elwood.
The Number of Two-Terminal Series-Parallel Networks
The Number of Two-Terminal Series-Parallel Networks
The offprint issue

The Number of Two-Terminal Series-Parallel Networks

[Cambridge, Massachusetts]: [Massachusetts Institute of Technology] August, 1942. 83-93, [1-blank] pages. 10 x 6 7/8 inches. Publisher's printed wrappers. Stapled near the spine (staples slightly rusty). Creasing to the spine, light sunning to the extremities. Very Good. Wraps. [28684]

The "Journal of Mathematics and Physics,” Vol 21, No. 2, August 1942, first published this paper, here offered in offprint form.

"One of the first attempts to list all electrical networks meeting certain specified conditions was made in 1892 by P. A. MacMahon who investigated combinations of resistances in series and in parallel, giving without proof a generating function from which the number of such combinations could be determined and a table of the numbers for combinations with 10 or less elements...the series-parallel networks are interesting in themselves in another setting, namely the design of switching circuits*. Here it becomes important to know how many elements are required to realize any switching function....These considerations have led us to work out a proof of MacMahon's generating function, which is given in full below; to develop recurences and schemes of computation from this and with which to extend MacMahon's table; to investigate the behavior of the series-parallel numbers when the number of elements is large, and finally to make the application to switching functions mentioned above." (pp 83-84)
* - references Shannon's thesis "A Symbolic Analysis of Relay and Switching Circuits."

PROVENANCE: The personal files of Claude E. Shannon (unmarked). There were seven examples of this offprint in Shannon's files, all with moderate amounts of soiling and damage.

Sloane and Wyner, "Claude Elwood Shannon Collected Papers," #14

Price: $350.00

See all items in Mathematics