# Rose Peltesohn

Rose Pauline Peltesohn
Born May 16, 1913
Berlin
Died March 21, 1998 (aged 84)
Kfar Saba
Fields Combinatorics
Institutions Berlin, Tel Aviv
Alma mater Humboldt University
Thesis Das Turnierproblem für Spiele zu je dreien (1936)
Doctoral advisor Issai Schur
Spouse Gerhard Peltesohn
Children Ruth (born 1940), Judith (born 1943).

Rose Pauline Peltesohn (16 May 1913 in Berlin – 21 March 1998 in Kfar Saba, Israel) was an Israeli mathematician of German origin.

## Life

Rose Peltesohn was the daughter of the physician Ludwig Peltesohn (1882–1937) and of Cilly Caro.[1] After graduation (Abitur) in March 1931 she studied mathematics and physics at the University of Berlin and got her Ph.D. in Mathematics at 1936 with Issai Schur [2] as supervisor (Das Turnierproblem für Spiele zu je dreien, The tournament problem for three person games). Her dissertation was valued opus valde laudabile(de). Being Jewish she emigrated through Italy to Palestine, arriving 1938. Between the years 1939–1942 she worked in a bank and later as a lawyer's secretary and translator in Tel Aviv. She married her cousin Gerhard Peltesohn, a lawyer (1909–1965), and both had two daughters, Ruth (born 1940) and Judith (born 1943).

## Solution of Heffter's Difference Problems

Peltesohn solved the Difference Problems of Lothar Heffter (de) (1896) in combinatorics in 1939.[3] A Difference Triple (abc) is defined as three different elements from the set ${\displaystyle 1,2,\dots ,v-1}$, whose sum ${\displaystyle {\bmod {v}}}$ equals zero (${\displaystyle a+b+c=0{\bmod {v}}}$) or for which one element ${\displaystyle {\bmod {v}}}$ equals the sum of the other two (${\displaystyle a+b=c{\bmod {v}}}$).

• First Difference Problem of Heffter: Let ${\displaystyle v=6m+1}$. Is there a partition of the set ${\displaystyle 1,2,\ldots ,3m}$ in difference triples?
• Second Difference Problem of Heffter: Let ${\displaystyle v=6m+3}$. Is there a partition of the set ${\displaystyle 1,2,\ldots ,2m,2m+2,\ldots ,3m+1}$ in difference triples ?

Following Peltesohn, such a partition exists with the exception of the case v = 9.

An example of the partition for ${\displaystyle v=13}$ is: ${\displaystyle (1,3,4)}$ (with ${\displaystyle 1+3=4{\bmod {1}}3}$) and ${\displaystyle (2,5,6)}$ (with ${\displaystyle 2+5+6=13=0{\bmod {1}}3}$).

The solution of the Difference Problem of Heffter also gives a construction of cyclic Steiner triple systems.