Tatyana van Aardenne-Ehrenfest

Tatyana Pavlovna van Aardenne-Ehrenfest, (née Ehrenfest; October 28, 1905 – November 29, 1984) was a Dutch mathematician. She is known for her contributions to De Bruijn sequences, low-discrepancy sequences, and the BEST theorem.

Tatyana van Aardennne-Ehrenfest
Van Aardenne-Ehrenfest in 1977 Photo courtesy of MFO
Born	Tatyana Pavlovna Ehrenfest (1905-10-28)October 28, 1905 Vienna, Austria
Died	November 29, 1984(1984-11-29) (aged 79) Dordrecht, Netherlands
Alma mater	University of Leiden
Known for	De Bruijn sequence BEST theorem
Parent(s)	Paul Ehrenfest Tatyana Afanasyeva
Scientific career
Fields	Mathematics
Thesis	Oppervlakken met scharen van gesloten geodetische lijnen  (1931)
Doctoral advisor	Willem van der Woude

In this Dutch name, the birth surname is Ehrenfest and the marital name is Van Aardenne-Ehrenfest.

In this article, Dutch capitalization is used for tussenvoegsels in Dutch family names. The first letter in Van Aardenne-Ehrenfest is capitalized unless it is preceded by a name, initial or title of nobility.

Early life and education

Tatyana Ehrenfest was born in Vienna in 1905 and spent her childhood in St Petersburg. She is the daughter of physicists Paul Ehrenfest and Tatyana Afanasyeva.

In 1912 the Ehrenfests moved to Leiden where her father succeeded Hendrik 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, advised by Willem van der Woude.^[1] 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 ${\displaystyle k}$ such that every length-${\displaystyle k}$ 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 Van Aardenne-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.

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