Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How close can we come to a parity function when there isn't one?   Consider a group G such that there is no homomorphism f:G to {+1,-1}. In that
case, how close can we come to such a homomorphism? We show that if f has zero
expectation, then the probability that f(xy) = f(x) f(y), where x, y are chosen
uniformly and independently from G, is at most 1/2(1+1/sqrt{d}), where d is the
dimension of G's smallest nontrivial irreducible representation. For the
alternating group A_n, for instance, d=n-1. On the other hand, A_n contains a
subgroup isomorphic to S_{n-2}, whose parity function we can extend to obtain
an f for which this probability is 1/2(1+1/{n \choose 2}). Thus the extent to
which f can be "more homomorphic" than a random function from A_n to {+1,-1}
lies between O(n^{-1/2}) and Omega(n^{-2}).

32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys