For a many-to-one matching market where firms have strict and q-responsive preferences, we give a characterization of the  strongly stable fractional matching set as the union of the convex hull of  connected sets of stable matchings  .
For a many-to-one matching market where firms have strict and -responsive preferences, we give a characterization of the set of strongly stable fractional matchings as the union of the convex hull of all connected sets of stable matchings . Also, we prove that a strongly stable fractional matching is represented as a convex combination of stable matchings that are ordered in the common preferences of all firms .
R
q-responsive
-responsive
A
set of
R
matching set
matchings
A
all
A
. Also, we prove that a strongly stable fractional matching is represented as a convex combination of stable matchings that are ordered in the common preferences of all firms