query: number of surjective functions from X to Y where card(Y)=k < n =card(X)
positive_passages.docid: 52348
positive_passages.text: Counting the number of surjections.
negative_passages.docid: 101993
negative_passages.text: The cardinality of a language over a set of variables $V$ with $\#V= κ$
negative_passages.docid: 146306
negative_passages.text: A continuous surjective function from $(0,1]$ onto $[0,1]$
negative_passages.docid: 102515
negative_passages.text: Counting functions between two sets
negative_passages.docid: 32340
negative_passages.text: Continuous bijections and their inverses
negative_passages.docid: 40868
negative_passages.text: Composition of two functions - Bijection
negative_passages.docid: 94407
negative_passages.text: Number of solutions for $x[1] + x[2] + \ldots + x[n] =k$
negative_passages.docid: 74730
negative_passages.text: Combinatorial Proof of ${{n}\choose{k}} {{k}\choose{j}} = {{n}\choose{j}} {{n-j}\choose{k-j}}$
negative_passages.docid: 30456
negative_passages.text: The number of $2 × 2$ invertible matrices with entries from field $\mathbb{Z}_p$
negative_passages.docid: 72750
negative_passages.text: Uncountable number of mutually disjoint countable sets in $\mathbb R$
negative_passages.docid: 74150
negative_passages.text: Problem on the number of generators of some ideals in $k[x,y,z]$
negative_passages.docid: 82003
negative_passages.text: Bijection between sets of ideals
negative_passages.docid: 21391
negative_passages.text: Proving Functions are Surjective
negative_passages.docid: 57221
negative_passages.text: counting the number of elements in a conjugacy class of $S_n$
negative_passages.docid: 97878
negative_passages.text: Are there uncountably many surjections from $\mathbb N$ to $\mathbb N$?
negative_passages.docid: 70282
negative_passages.text: Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$
negative_passages.docid: 17348
negative_passages.text: Number of non-decreasing functions?