Rose Peltesohn

Rose Pauline Peltesohn (born May 16, 1913 in Berlin ; † March 21, 1998 in Kfar Saba , Israel ) was a German-Israeli mathematician.

Rose Peltesohn

Life

Peltesohn was the daughter of the doctor Ludwig Peltesohn (1882–1937) and Zili Caro. After graduating from high school in 1931, she studied at the University of Berlin and received her doctorate in mathematics from Issai Schur in 1936 ( the tournament problem for games of three , a special case of Baranyai's theorem, which was later proven ). The dissertation received the grade opus valde laudabile . Then she emigrated as a Jew via Italy to Palestine, where she arrived in 1938. She worked there in a bank and later as a law clerk and translator in Tel Aviv. She married her cousin Gerhard Peltesohn (1909–1965), with whom she had two daughters, born in 1940 and 1943.

Solving Heffter's difference problems

In 1939 she solved Lothar Heffter's (1896) difference problems in combinatorics. A difference triple (a, b, c) is defined from three different elements of the set whose sum is zero ( ) or where one element is the sum of the other two ( ). ${\ displaystyle 1,2, ..., v-1}$ ${\ displaystyle mod \ v}$ ${\ displaystyle a + b + c = 0 \ mod \ v}$ ${\ displaystyle mod \ v}$ ${\ displaystyle a + b = c \, mod \ v}$

First difference problem from Heffter: Sei . Can the set be broken down into difference triples? ${\ displaystyle v = 6m + 1}$ ${\ displaystyle 1,2, ..., 3m}$
Second difference problem from Heffter: Sei . Can the set be broken down into difference triples? ${\ displaystyle v = 6m + 3}$ ${\ displaystyle 1,2, .., 2m, 2m + 2, ..., 3m + 1}$

According to Peltesohn, such a decomposition is possible except for v = 9.

An example of the decomposition in the case : (with ) and (with ). ${\ displaystyle v = 13}$ ${\ displaystyle (1,3,4)}$ ${\ displaystyle 1 + 3 = 4 \ mod \ 13}$ ${\ displaystyle (2,5,6)}$ ${\ displaystyle 2 + 5 + 6 = 13 = 0 \ mod \ 13}$

The solution to Heffter's difference problems is also provided by a construction of cyclic Steiner-Triple systems .

literature

Maximilian Pinl Colleagues in a Dark Time , Annual Report DMV, Volume 71, 1969, pp. 188-189
Renate Tobies : Biographical Lexicon in Mathematics for PhDs from WS 1907/08 to WS 1944/45, Rauner Verlag 2006

Individual evidence

^ A solution to the two Hefftersian difference problems, Compositio Mathematica, Volume 6, 1939, pp. 251-257

personal data
SURNAME	Peltesohn, rose
ALTERNATIVE NAMES	Peltesohn, Rose Pauline
BRIEF DESCRIPTION	Israeli mathematician
DATE OF BIRTH	May 16, 1913
PLACE OF BIRTH	Berlin
DATE OF DEATH	March 21, 1998
Place of death	Kfar Saba

[1] A solution to the two Hefftersian difference problems, Compositio Mathematica, Volume 6, 1939, pp. 251-257