Math 681 Test 2 Review
W/KmDLet M be a matroid on the set E and k be a nonnegative integer not exceeding r(M
W iDene me) 2 23m) 2*" U {0} by me) (X) = min{k,r(X Prove that m.) is the rank
function of a matroid E of rank 1:.
(J Finish the denition. Let M b
Name: ,
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Math 681 Final Review
. Prove that (E,I) is a matroid if and only I satises (I 2) and the
following two conditions:
(I 1) I % (I)
(I3)' If I1 and I2 are in I and ]I21 2 [I1] + 1, then there is an
element 6 of I2 - I1 such that I1 U 8 E I
. P
' Name: .K
,Math 681 Quiz 1
1. Prove that (19,1) is a matroid if and oniy I satisfies (I2) and the foiiowing two conditions:
(my I 55 0
a
(I3) 11°11 and I2 are in 1' and '12; = [Ill + 1, then there is an element 6 of [2 - 11 such thaw
t
IIUeEI I
9 X