Wedderburn-Etherington number

Wedderburn-Etherington number

In graph theory, the Wedderburn-Etherington numbers count how many weakly binary trees can be constructed: that is, the number of trees for which each graph vertex (not counting the root) is adjacent to no more than three other such vertices, for a given number of nodes. The first few Wedderburn-Etherington numbers are

:1, 1, 1, 2, 3, 6, 11, 23, 46, 98, 207, 451, 983, 2179, 4850, 10905, 24631, 56011, 127912, 293547, 676157, 1563372, 3626149, 8436379, 19680277, 46026618, 107890609, 253450711, 596572387, 1406818759, 3323236238, 7862958391.

The first Wedderburn-Etherington numbers that are primes are

:2, 3, 11, 23, 983, 2179, 24631, 3626149, 253450711, 596572387.

References

* S. J. Cyvin et al, "Enumeration of constitutional isomers of polyenes," "J. Molec. Structure (Theochem)" 357 (1995): 255 - 261
* I. M. H. Etherington, "Non-associate powers and a functional equation," "Math. Gaz." 21 (1937): 36 - 39, 153
* I. M. H. Etherington, "On non-associative combinations," "Proc. Royal Soc. Edinburgh", 59 2 (1939): 153 - 162.
* S. R. Finch, "Mathematical Constants". Cambridge: Cambridge University Press (2003): 295 - 316
* F. Murtagh, "Counting dendrograms: a survey," "Discrete Applied Mathematics" 7 (1984): 191 - 199
* J. H. M. Wedderburn, "The functional equation g(x^2) = 2ax + [ g(x) ] ^2" "Ann. Math." 24 (1923): 121 - 140

External links

*
* (prime subsequence)


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать реферат

Look at other dictionaries:

  • Etherington — may refer to: *William or Bill Etherington, a British politician. *Matthew Etherington, an English footballer. *A Wedderburn Etherington number. *Lady Alexandra Etherington, a member of the British aristocracy. *Amelia Mary Carnegie Etherington,… …   Wikipedia

  • Wedderburn — There are a number of towns called Wedderburn:*Wedderburn, Victoria, Australia *Wedderburn, New South Wales, Australia *Wedderburn, Oregon, United States *Wedderburn, Otago, New ZealandOther places named Wedderburn: *Wedderburn Castle, in… …   Wikipedia

  • 10000 (number) — Number number = 10000 prev = 9999 next = 100000 range = 10000 100000 cardinal = 10000 ordinal = th ordinal text = ten thousandth numeral = decamillesimal factorization = 2^4 cdot 5^4 prime = divisor = roman = overline|X unicode = overline|X, ↂ… …   Wikipedia

  • 20000 (number) — Number number = 20000 range = 10000 100000 cardinal = 20000 ordinal = th ordinal text = twenty thousandth factorization = 2^5 cdot 5^4 bin = 100111000100000 oct = 47040 hex = 4E2020,000 (twenty thousand) is the number that comes after 19,999 and… …   Wikipedia

  • 50000 (number) — Number number = 50000 range = 10000 100000 cardinal = 50000 ordinal = th ordinal text = fifty thousandth factorization = 2^4 cdot 5^5 bin = 1100001101010000 oct = 141520 hex = C35050,000 (fifty thousand) is the number that comes after 49,999 and… …   Wikipedia

  • 207 (number) — Number|number = 207 range = 200s cardinal = two hundred [and] seven ordinal = th ordinal text = two hundred [and] seventh numeral = factorization = 3^2 imes 23 prime = divisor = 1, 3, 9, 23, 207 roman = CCVII unicode = greek prefix = latin prefix …   Wikipedia

  • Joseph Wedderburn — Infobox Scientist box width = 300px name = Joseph Wedderburn image width = 300px caption = Joseph Henry Maclagan Wedderburn (1882 1948) birth date = birth date|1882|02|02 birth place = Forfar, Angus, Scotland death date = death date and… …   Wikipedia

  • 100000 (number) — List of numbers – Integers 10000 100000 1000000 Cardinal One hundred thousand Ordinal One hundred thousandth Factorization 25 · 55 Roman numeral C Roman numeral (Unicode) …   Wikipedia

  • 1000000000 (number) — List of numbers – Integers 100000000 1000000000 10000000000 Cardinal One billion (short scale) One thousand million (long scale) Ordinal One billionth (short scale) Factorization 29 · 59 Binary 111011100110101100101000000000 He …   Wikipedia

  • 100000000 (number) — 100 million redirects here. For the song by Birdman, see 100 Million. One hundred million (100,000,000) is the natural number following 99999999 and preceding 100000001. List of numbers – Integers 10000000 100000000 1000000000 Cardinal One… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”