366 research outputs found
Counting packings of generic subsets in finite groups
A packing of subsets in a group is a
sequence such that are
disjoint subsets of . We give a formula for the number of packings if the
group is finite and if the subsets satisfy
a genericity condition. This formula can be seen as a generalization of the
falling factorials which encode the number of packings in the case where all
the sets are singletons
Counting invertible Schr\"odinger Operators over Finite Fields for Trees, Cycles and Complete Graphs
We count invertible Schr\"odinger operators (perturbations by diagonal
matrices of the adjacency matrix) over finite fieldsfor trees, cycles and
complete graphs.This is achieved for trees through the definition and use of
local invariants (algebraic constructions of perhapsindependent
interest).Cycles and complete graphs are treated by ad hoc methods.Comment: Final version to appear in Electronic Journal of Combinatoric
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