Tatyana Pavlovna van Aardenne-Ehrenfest, (; October 28, 1905 – November 29, 1984) was a Dutch

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. She is known for her contributions to

De Bruijn sequence In combinatorics, combinatorial mathematics, a de Bruijn sequence of order ''n'' on a size-''k'' alphabet (computer science), alphabet ''A'' is a cyclic sequence in which every possible length-''n'' String (computer science)#Formal theory, stri ...

low-discrepancy sequence In mathematics, a low-discrepancy sequence is a sequence with the property that for all values of N, its subsequence x_1, \ldots, x_N has a low discrepancy of a sequence, discrepancy. Roughly speaking, the discrepancy of a sequence is low if the p ...

s, and the

BEST theorem In graph theory, a part of discrete mathematics, the BEST theorem gives a product formula for the number of Eulerian circuits in directed (oriented) graphs. The name is an acronym of the names of people who discovered it: N. G. de Bruijn, Tatya ...

Early life and education

Tatyana Ehrenfest was born in Vienna in 1905 and spent her childhood in

St Petersburg Saint Petersburg, formerly known as Petrograd and later Leningrad, is the List of cities and towns in Russia by population, second-largest city in Russia after Moscow. It is situated on the Neva, River Neva, at the head of the Gulf of Finland ...

. She is the daughter of physicists

Paul Ehrenfest Paul Ehrenfest (; 18 January 1880 – 25 September 1933) was an Austrian Theoretical physics, theoretical physicist who made major contributions to statistical mechanics and its relation to quantum physics, quantum mechanics, including the theory ...

and

Tatyana Afanasyeva Tatyana Alexeyevna Afanasyeva-Ehrenfest (; ; 19 November 1876 – 14 April 1964) was a Russian-Dutch mathematician and physicist who made contributions to the fields of statistical mechanics and statistical thermodynamics with her husband Paul E ...

. In 1912 the Ehrenfests moved to

Leiden Leiden ( ; ; in English language, English and Archaism, archaic Dutch language, Dutch also Leyden) is a List of cities in the Netherlands by province, city and List of municipalities of the Netherlands, municipality in the Provinces of the Nethe ...

where her father succeeded

Hendrik Lorentz Hendrik Antoon Lorentz ( ; ; 18 July 1853 – 4 February 1928) was a Dutch theoretical physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for their discovery and theoretical explanation of the Zeeman effect. He derive ...

as professor at the

University of Leiden Leiden University (abbreviated as ''LEI''; ) is a public research university in Leiden, Netherlands. Established in 1575 by William, Prince of Orange as a Protestant institution, it holds the distinction of being the oldest university in the Neth ...

. Until 1917 she was home schooled; after that, she attended the Gymnasium in Leiden and passed the

final exams An examination (exam or evaluation) or test is an educational assessment intended to measure a test-taker's knowledge, skill, aptitude, physical fitness, or classification in many other topics (e.g., beliefs). A test may be administered verba ...

in 1922. She studied mathematics and physics at the University of Leiden. In 1928 she went to

Göttingen Göttingen (, ; ; ) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. According to the 2022 German census, t ...

where she took courses from

Harald Bohr Harald August Bohr (22 April 1887 – 22 January 1951) was a Danish mathematician and footballer. After receiving his doctorate in 1910, Bohr became an eminent mathematician, founding the field of almost periodic functions. His brother was the ...

and

Max Born Max Born (; 11 December 1882 – 5 January 1970) was a German-British theoretical physicist who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics, and supervised the work of a ...

. On December 8, 1931, she obtained her Ph.D. in Leiden, advised by

Willem van der Woude Willem van der Woude (15 January 1876 – 23 September 1974) was a Dutch mathematician and ''rector magnificus'' (chancellor) of the University of Leiden. Education and career Van der Woude studied at the University of Groningen, and subsequen ...

. After that, she was never employed and, in particular, never held any academic position.

Contributions

s are cyclic sequences of symbols for a given alphabet and parameter

k

such that every length-

k

subsequence occurs exactly once within them. They are named after

Nicolaas Govert de Bruijn Nicolaas Govert "Dick" de Bruijn (; 9 July 1918 – 17 February 2012) was a Dutch mathematician, noted for his many contributions in the fields of analysis, number theory, combinatorics and logic.

, 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

, also known as the de Bruijn–van Aardenne-Ehrenfest–Smith–Tutte theorem, relates

Euler tour In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices). Similarly, an Eulerian circuit or Eulerian cycle is an Eulerian trail that starts and end ...

s and

spanning tree In the mathematical field of graph theory, a spanning tree ''T'' of an undirected graph ''G'' is a subgraph that is a tree which includes all of the vertices of ''G''. In general, a graph may have several spanning trees, but a graph that is no ...

s 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

References

# ''Oppervlakken met scharen van gesloten geodetische lijnen'', Thesis, Leiden, 1931. # N.G. de Bruijn
In memoriam T. van Aardenne-Ehrenfest, 1905–1984
''Nieuw Archief voor Wiskunde (4)'', Vol.3, (1985) 235–236. # # # Eric W. Weisstein
Discrepancy Theorem
From MathWorld – A Wolfram Web Resource. {{DEFAULTSORT:Ehrenfest, Tatyana 1905 births 1984 deaths 20th-century Dutch mathematicians Dutch Jews Combinatorialists People from Leiden Austrian emigrants to the Netherlands Austrian Jews Austrian people of Ukrainian descent Austrian people of Russian descent 20th-century women mathematicians Expatriates from Austria-Hungary in the Russian Empire