Start Discovering Solved Questions and Your Course Assignments
TextBooks Included
Active Tutors
Asked Questions
Answered Questions
in this exercise we prove a generalization of brouwers fixed point theorem to compact sets that are not necessarily
the following tables depict the preferences of three universities regarding a set of applicants and the preferences of
suppose that a population of size 3n is partitioned into three subsets n contractors n carpenters and n plumbers each
let x0 x1 x2nbspbe three vectors in rn prove that these vectors are affine independent if and only if none of them is a
prove that the boundary of a simplex s is the set of all the points y in s whose barycentric coordinate representation
prove that if the result of the mens courtship algorithm yields the same result as the womens courtship algorithm then
given a stable matching of n men and n womena is it possible to find three pairs such that if the matching among them
in juliuss list of preferences agrippina appears first messalina appears second and cleopatra appears thirdsuppose
in this exercise we consider a situation with n men and n womena prove that if in stage t of the mens courtship
suppose that fara is preferred by every man to all the other womenprove that under every stable matching fara is
suppose that the number of men equals the number of women and that vera is last on the preference list of every
in this exercise we present a family of algorithms each of which produces the mens courtship matching and contains the
1 show by example that if a and b are two matchings not necessarily stable then a orw b is not necessarily a matching2
suppose that the matching problem is to match nm men to nw women where nwa describe in detail the generalization of the
let a be a matching not necessarily stable and let maom be the set of men who prefer the women to whom they are matched
ron and veronica need to choose a name for their newborn daughter after giving the matter much thought they have
a committee comprised of 15 members is called upon to choose the prettiest color red blue or yellow the committee
the following electoral method is used to choose the mayor of whoville every resident ranks the candidates from most
1 prove that every complete irreflexive and transitive relation is asymmetric ifxnbspne y then x gt y if and only if
consider the following system of preferences recall that the preferences of the women appear in the lower right side of
suppose that the number of men equals the number of women prove the following claims or provide counterexamplesa for
gary is at the top of gails preference list and gail is at the top of garys preference list prove that in every stable
dan is at the bottom of donnas preference list and donna is at the bottom of dans preference list is it possible that
prove that if romeo and juliet are matched to each other under both the mens courtship and the womens courtship
the condorcet method the french mathematician condorcet proposed the following method for determining a social