query: Number of nondecreasing functions from $\{1,2,\dots,n\}$ to $\{1,2,\dots,n\}$
positive_passages.docid: 17348
positive_passages.text: Number of non-decreasing functions?
negative_passages.docid: 82222
negative_passages.text: Determine the number of functions $f: \{1,2,3....,1999\}\to \{2000,2001,2002,2003\}$satisfying the condition that $f(1)+f(2)+...f(1999)$ is odd.
negative_passages.docid: 40566
negative_passages.text: Counting surjective functions
negative_passages.docid: 7938
negative_passages.text: Number of Homomorphisms from $\Bbb{Z}_m$ to $\Bbb{Z}_n$
negative_passages.docid: 80744
negative_passages.text: What is the number of strings at size $n$ that is constructed from ${a,b,c,d}$ and there is an even num of $a$
negative_passages.docid: 146491
negative_passages.text: Number of solutions of $x_1+x_2+\dots+x_k=n$ with $x_i\le r$
negative_passages.docid: 85658
negative_passages.text: Number of onto functions
negative_passages.docid: 65978
negative_passages.text: How many subsets does the set $\{1, 2, \dots , n\}$ have that contain no two consecutive integers if $1$ and $n$ also count as consecutive?
negative_passages.docid: 115973
negative_passages.text: Computing the number of nonisomorphic finite abelian groups of order $n$
negative_passages.docid: 92554
negative_passages.text: How many lattice paths are there from $(0,0)$ to $(2n,2n)$ that avoids odd points
negative_passages.docid: 134440
negative_passages.text: An unexpected application of non-trivial combinatorics
negative_passages.docid: 133017
negative_passages.text: Prove that $n^n>1\times3\times5\times7\times \dots\times(2n-1)$
negative_passages.docid: 52348
negative_passages.text: Counting the number of surjections.
negative_passages.docid: 141984
negative_passages.text: Find the number of homomorphisms between $\mathbb{Z}_m$ and $\mathbb{Z}_n$
negative_passages.docid: 128766
negative_passages.text: Show that the set of functions $\mathbb{N}\to\{0,1\}$ is not countable
negative_passages.docid: 40486
negative_passages.text: Number of One-to-One Functions
negative_passages.docid: 144890
negative_passages.text: Recurrence $f_{n+2}=af_{n+1}+bf_n$