DocumentCode :
1061740
Title :
There Are No Further Counterexamples to S. Piccard´s Theorem
Author :
Bekir, Ahmad ; Golomb, Solomon W.
Author_Institution :
Pratt & Whitney Rocketdyne, Los Angeles
Volume :
53
Issue :
8
fYear :
2007
Firstpage :
2864
Lastpage :
2867
Abstract :
In 1977, G. S. Bloom, in the J. Combinatorial Theory, showed that Sophie Piccard´s ldquotheoremrdquo had counterexamples for six-mark rulers. Subsequent research into finding additional counterexamples has focused on a variety of computer algorithms, such as searching the space of rulers with relatively few marks in an attempt to find another counterexample. Recent analytic effort has made use of Golomb´s ldquopolynomial method,rdquo which made strides in eliminating specific types of rulers which cannot contain counterexamples. The question as to whether other larger length ruler counterexamples exist, however, was left unanswered. In this correspondence, a geometric manipulation of the ldquopolynomial methodrdquo is used to demonstrate that no additional counterexamples are possible.
Keywords :
combinatorial mathematics; polynomials; Golomb polynomial method; Sophie Piccard theorem; computer algorithms; geometric manipulation; six-mark rulers; spanning rulers; Bonding; Crystallography; Extraterrestrial measurements; Length measurement; Mirrors; Radar applications; Radar theory; Radio astronomy; X-ray diffraction; X-ray imaging; Counterexample; Golomb; Piccard; Sophie; ruler; spanning;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.2007.899468
Filename :
4276910
Link To Document :
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