Let q be a prime power and let S(F) be the set of subspaces of F....

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Let q be a prime power and let S(F) be the set of subspaces of F. Viewing S(F2) as a poset ordered by containment, show that µ({0}, Fņ) = (−1)^q(²) where U, V = S(Fn) and k - dim(V) – dim(U). (Hint: Use the q-binomial Theorem with t = -1. You may assume S(F) is a lattice.) Let q be a prime power and let S(F) be the set of subspaces of F. Viewing S(F2) as a poset ordered by containment, show that µ({0}, Fņ) = (−1)^q(²) where U, V = S(Fn) and k - dim(V) – dim(U). (Hint: Use the q-binomial Theorem with t = -1. You may assume S(F) is a lattice.) Let q be a prime power and let S(F) be the set of subspaces of F. Viewing S(F2) as a poset ordered by containment, show that µ({0}, Fņ) = (−1)^q(²) where U, V = S(Fn) and k - dim(V) – dim(U). (Hint: Use the q-binomial Theorem with t = -1. You may assume S(F) is a lattice.) Let q be a prime power and let S(F) be the set of subspaces of F. Viewing S(F2) as a poset ordered by containment, show that µ({0}, Fņ) = (−1)^q(²) where U, V = S(Fn) and k - dim(V) – dim(U). (Hint: Use the q-binomial Theorem with t = -1. You may assume S(F) is a lattice.)

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To show that 0 F 12 where U V SFn and k dimV dimU we can use the qbinomial theorem ... View the full answer