Math Problem Statement
By [ π ] [n]we denote the set { 1 , β¦ , π } {1,β¦,n}. A function π : [ π ] β [ π ] f:[m]β[n] is called monotone if π ( π ) β€ π ( π ) f(i)β€f(j)whenever π < π i<j. Let π ( π , π ) S(m,n) be the number of monotone injective functions from [ π ] [m] to [ π ] [n]. What is the number of monotone injective functions from [ 10 ] [10] to [ 20 ] [20]?
Solution
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Monotone Functions
Injective Functions
Binomial Coefficient
Formulas
S(m,n) = C(n, m) = (n! / (m!(n-m)!))
Theorems
Binomial Coefficient
Suitable Grade Level
Undergraduate - Discrete Mathematics