**Combinatorics and Computing Weekly Seminar**

Partitions into Pairs with Prescribed Differences

Ali Mohammadian, IPM

22 MAY 2024
14:00 - 15:00
Consider the following two general questions:
-For an Abelian group $A$ of order $2n$ and nonzero elements $d_1, ldots, d_n$ of $A$, is it always possible to partition $A$ into pairs such that the difference between the two elements of the $i$th pair is equal to $d_i$?

-For an Abelian group $A$ of order $2n+1$ and nonzero elements $d_1, ldots, d_n$ of $A$, is it always possible to partition $Asetminus{0}$ into pairs such that the difference between the two elements of the $i$th pair is equal to $d_i$?

In this talk, we briefly review some known results and open conjectures regarding the above questions.

https://us06web.zoom.us/j/89600366073?pwd=RMHt0eGdvGtkaDBG1Me3y8bOLgooGh.1

Meeting ID : 896 0036 6073

Passcode : 290109

**Venue**: Niavaran, Lecture Hall 3