2
votes
0answers
23 views

Counting homomorphisms by the order of their images

I am trying to count homomorphisms from $\mathbb Z^r$ to $(\mathbb Z/m)^n$ while keeping track of the order of the image of each map. In other words, for each integer $k$ dividing $m^n$, I want to ...
1
vote
1answer
104 views

Number of Inequivalent Difference Sets In Elementary Abelian 2-groups

I have reason to believe that there is only one$(2^{2s+2},2^{2s+1}-2^s,2^{2s}-2^s)$- difference set (based on experimentation in GAP), up to equivalence/complementation, in any elementary 2-group of ...
0
votes
1answer
58 views

Counting commuting Pauli Strings of a certain weight

Let a $n-$length pauli string represent any tensor product of finitely many pauli matrices, Ex: $X\otimes Z\otimes \mathbb{I}\otimes Y\otimes \mathbb{I}\otimes X\otimes\cdots\otimes Z$ where the ...
0
votes
1answer
51 views

If E is a subset of a lattice closed under addition then is the intersection of E with the opposite of some translate finite?

this seems intuitive to me but I'm struggling to prove it (is it false?). Let $E$ be a subset of a lattice (free abelian group of finite rank) closed under addition, containing the origin and such ...