2 citations · 11 across the 11 of their papers we have counts for
11 papers
Subset Sum Instances in ZFC Limbo
S. Gill Williamson
Our main result, Theorem 2.5, shows the existence of a vast infinity of subset sum problems solvable in polynomial time. The only proof we have of this result uses the ZFC independ…
On the difficulty of proving P equals NP in ZFC
S. Gill Williamson
Harvey Friedman, in his remarkable paper Finite functions and the necessary use of large cardinals, Ann. Math. 148:803-893, 1998 and in a technical report, Applications of large ca…
ZFC independence and subset sum
S. Gill Williamson
We study recursively defined functions associated with directed graphs on the k dimensional nonnegative integral lattice. The existence of certain combinatorial structures associat…
Lattice exit models
S. Gill Williamson
We discuss a class of problems which we call lattice exit models. At one level, these problems provide undergraduate level exercises in labeling the vertices of graphs (e.g., depth…
Tensor spaces - the basics
S. Gill Williamson
We present the basic concepts of tensor products of vector spaces, emphasizing linear algebraic and combinatorial techniques as needed for applied areas of research. The topics inc…
The common-submatrix Laplace expansion
S. Gill Williamson
We state and prove a classical version of the Laplace expansion theorem where all submatrices in the expansion are restricted to contain a specified common submatrix (CSM). The res…