Tatyana Pavlovna Ehrenfest

Tatyana Pavlovna Ehrenfest, later van Aardenne-Ehrenfest, (Vienna, October 28, 1905 – Dordrecht, November 29, 1984) was a Dutch mathematician. She was the daughter of Paul Ehrenfest (1880–1933) and Tatyana Alexeyevna Afanasyeva (1876–1964).

van Aardenne-Ehrenfest in 1977
Photo courtesy of MFO

Under her married name, Tanja van Aardenne-Ehrenfest, she is known for her contributions to De Bruijn sequences, low-discrepancy sequences, and the BEST theorem.

Education

Tatyana Ehrenfest was born in Vienna, and spent her childhood in St Petersburg. In 1912 the Ehrenfests moved to Leiden where her father succeeded H.A. Lorentz as professor at the University of Leiden. Until 1917 she was home schooled, after that she attended the Gymnasium in Leiden and passed the final exams in 1922. She studied mathematics and physics at the University of Leiden. In 1928 she went to Göttingen where she took courses from Harald Bohr and Max Born. On December 8, 1931 she obtained her Ph.D. in Leiden. After that, she was never employed and, in particular, never held any academic position.

Contributions

De Bruijn sequences are cyclic sequences of symbols for a given alphabet and parameter such that every length- subsequence occurs exactly once within them. They are named after Nicolaas Govert de Bruijn, despite their earlier discovery (for binary alphabets) by Camille Flye Sainte-Marie. De Bruijn and Ehrenfest jointly published the first investigation into de Bruijn sequences for larger alphabets, in 1951.

The BEST theorem, also known as the de Bruijn-van Aardenne Ehrenfest-Smith-Tutte theorem, relates Euler tours and spanning trees in directed graphs, and gives a product formula for their number. It is a variant of an earlier formula of Smith and Tutte, and was published by de Bruijn and Ehrenfest in the same paper as their work on de Bruijn sequences.

Ehrenfest is also known for her proof of a lower bound on low-discrepancy sequences.

gollark: New esolang: DWIW.DWIW means "Do What I Want".
gollark: ``` TrumpScript boycotts OS X and all Apple products until such time as Apple gives cellphone info to authorities regarding radical Islamic terrorist couple from Cal. The language is completely case insensitive. If the running computer is from China, TrumpScript will not compile. We don't want them stealing our American technological secrets. By constructing a wall (providing the --Wall flag), TrumpScript will refuse to run on machines with Mexican locales Warns you if you have any Communists masquerading as legitimate "SSL Certificates" from China on your system. Won't run in root mode because America doesn't need your help being great. Trump is all we need. Easy to type with small handsIf you find you can't get any TrumpScript to run on your computer (probably because we disallow the two most popular operating systems), you can specify the --shut_up flag to let the interpreter know you just want your code to run, damn it.```
gollark: ```Our language includes several convenient features, perfect for any aspiring Presidential candidate including: No floating point numbers, only integers. America never does anything halfway. All numbers must be strictly greater than 1 million. The small stuff is inconsequential to us. There are no import statements allowed. All code has to be home-grown and American made. Instead of True and False, we have the keywords fact and lie. Only the most popular English words, Trump's favorite words, and current politician names can be used as variable names. Error messages are mostly quotes directly taken from Trump himself. All programs must end with America is great. Our language will automatically correct Forbes' $4.5B to $10B. In its raw form, TrumpScript is not compatible with Windows, because Trump isn't the type of guy to believe in PC.```
gollark: https://github.com/samshadwell/TrumpScript
gollark: TrumpScript.

References
  1. ^ Oppervlakken met scharen van gesloten geodetische lijnen, Thesis, Leiden, 1931.
  2. ^ N.G. de Bruijn, In memoriam T. van Aardenne-Ehrenfest, 1905–1984, Nieuw Archief voor Wiskunde (4), Vol.3, (1985) 235–236.
  3. ^ Stanley, Richard P. (2018), Algebraic Combinatorics: Walks, Trees, Tableaux, and More, Undergraduate Texts in Mathematics (2nd ed.), Springer, p. 160, ISBN 9783319771731
  4. ^ Jackson, D. M.; Goulden, I. P. (1979), "Sequence enumeration and the de Bruijn–van Aardenne-Ehrenfest–Smith–Tutte theorem", Canadian Journal of Mathematics, 31 (3): 488–495, doi:10.4153/CJM-1979-054-x, MR 0536359
  5. ^ Eric W. Weisstein. Discrepancy Theorem. From MathWorld – A Wolfram Web Resource.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.