query: Counting functions satisfying $f(j)<f(i)+j-i$ for all $i<j$
positive_passages.docid: 25563
positive_passages.text: Count number of increasing functions, nondecreasing functions $f: \{1, 2, 3, \ldots, n\} \to \{1, 2, 3, \ldots, m\}$, with $m \geq n$.
negative_passages.docid: 57221
negative_passages.text: counting the number of elements in a conjugacy class of $S_n$
negative_passages.docid: 122329
negative_passages.text: Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
negative_passages.docid: 84301
negative_passages.text: Showing that some Function on the Unit Disc is injective
negative_passages.docid: 66772
negative_passages.text: $f(f(x)f(y))+f(x+y)=f(xy)$
negative_passages.docid: 44670
negative_passages.text: Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(x+y)=f(x)+f(y)$
negative_passages.docid: 38568
negative_passages.text: Finding the number of zeros of $f(z) = z^n$ if $|f(z)| < 1 $ for all $z$ with $|z|=1$.
negative_passages.docid: 118595
negative_passages.text: Proving that a set is countable by finding a bijection
negative_passages.docid: 39090
negative_passages.text: Finding functions such that $f(g(x)) = f(x)g(x)$
negative_passages.docid: 131692
negative_passages.text: How to show that $f_{0}f_{1}+f_{1}f_{2}+...+f_{2n-1}f_{2n} = f^{2}_{2n}$
negative_passages.docid: 81799
negative_passages.text: Examples of functions where $f(ab)=f(a)+f(b)$
negative_passages.docid: 79490
negative_passages.text: Proving the set of points at which a function diverges to $\infty$ is countable
negative_passages.docid: 146436
negative_passages.text: Cardinality of the set of bijective functions on $\mathbb{N}$?
negative_passages.docid: 141225
negative_passages.text: Number of all bijective functions from A to A.
negative_passages.docid: 122149
negative_passages.text: How to prove that $\sum_{i<j}(X_i-X_j)^2=n\sum_{i=1}^{n}(X_i-\bar{X})^2$
negative_passages.docid: 28927
negative_passages.text: IMO 1987 - function such that $f(f(n))=n+1987$
negative_passages.docid: 41448
negative_passages.text: Counting set for generating functions