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1 a hole is cut through the center of a sphere of radius r the height of the remaining spherical ring is h find the
assignment 2-1 recall that a tournament is a complete graph with directed edges so we think of the vertices as players
assignment 1-1 for a pair of vertices u v in a graph g the distance between u and v denoted du v is the number of edges
math 121c topics in geometric combinatorics spring 2012 problems-a suppose x1 x2 xn sub r2 are convex sets such
math 121c topics in geometric combinatorics spring 2012 problems-let m s i be a matroida prove that mlowast is a
math 121c topics in geometric combinatorics spring 2012 problems-for pi isin sn the descent set of pi isdespi j isin n
math 121c topics in geometric combinatorics spring 2012 problems-a let g be a graph vertices 1 2 n the graphical
math 121c topics in geometric combinatorics spring 2012 problems-a let l be a finite lattice and let fx s be a c-valued
math 121c topics in geometric combinatorics spring 2012 problems-prove that f0 f3 there exists a 4 dimensional polytope
math 121c topics in geometric combinatorics spring 2012 problems-consider the polytope bn sub rntimesn consisting of n
math 121c topics in geometric combinatorics spring 2012 problems-a suppose p sub rn is a full dimensional simple
math 121c topics in geometric combinatorics spring 2012 problems-a let p q sub rn be two n-dimensional polytopes we say
math 121c topics in geometric combinatorics spring 2012 problems-a set s sub rn is a convex cone if it is a convex set
question 1 the general cereal company believes that at least 20 of customers prefer its cereal to other brands of
assignment 8-1 let a be a finite set with subsets a1 an and let d1 d2 dn be positive integers show that there
assignment 7-1 a let g be a graph on n vertices prove that g is connected if and only if all the non-diagonal entries
assignment 6-1 determine the number of ways to color the faces of the following solid figure where two colorings are
assignment 5-1 a what is the order of the permutation 1348679 in s9 how many permutations have the same cycle type as
assignment 4-1 for each of the following sequences a0 a1 a2 determine a closed form for the generating series ax
assignment 3-1 a the game of motzhee consists of rolling five 8-sided dice each die of a differing color each of whose
assignment 2-1 a solve the congruence equation 19x equiv 3 mod 32b compute 1905189 mod 2741 using at most 12
assignment 1-1 a using the euclidean algorithm determine gcd248399 282041b a plane has capacity 15 921 pounds a company
assignment 8-1 a prove that a sphere with radius r has volume 43 pir3b determine the volume of the solid obtained by
assignment 6-1 for any real number x x be the greatest integer less than or equal to x for example 321 3 and 495 4
assignment 5-1 use the mean value theorem to show that19 lt radic66 - 8 lt 182 in this problem we will use the mean