query: Counting 2-partitions of $\{1, 2, \cdots, n\}$ of equal size and sum
positive_passages.docid: 144779
positive_passages.text: The number of ways to represent $(n^2+n)/4$ as a sum of $n/2$ distinct integers in $1,\dots,n$
negative_passages.docid: 11967
negative_passages.text: number of subsets of even and odd
negative_passages.docid: 117862
negative_passages.text: Number of partitions of an $n$-element set into $k$ classes
negative_passages.docid: 106896
negative_passages.text: Number of solutions of $x_1+2x_2+\cdots+kx_k=n$?
negative_passages.docid: 82872
negative_passages.text: Combinatorial proof involving partitions and generating functions
negative_passages.docid: 151520
negative_passages.text: About the parity of the product $(a_1-1)(a_2-2)\cdots(a_n-n)$
negative_passages.docid: 92941
negative_passages.text: # of partitions of $n$ into at most $r$ positive integers $=$ # of partitions of $n + r$ into exactly $r$ positive integers?
negative_passages.docid: 156383
negative_passages.text: Proving a combinatorial identity without double counting
negative_passages.docid: 63571
negative_passages.text: The Mississipi counting problem, this time in circle
negative_passages.docid: 99868
negative_passages.text: Sum(Partition(Binary String)) = $2^k$
negative_passages.docid: 107614
negative_passages.text: Partitioning an infinite set
negative_passages.docid: 142477
negative_passages.text: Closed-form expression for the number of $k$-permutations of length $n$. Duplicates allowed!
negative_passages.docid: 134921
negative_passages.text: Find the number of all subsets of $\{1, 2, \ldots,2015\}$ with $n$ elements such that the sum of the elements in the subset is divisible by 5
negative_passages.docid: 3392
negative_passages.text: Sum of products of elements of nonempty subsets of A set
negative_passages.docid: 112374
negative_passages.text: Evaluate $ \binom{n}{0}+\binom{n}{2}+\binom{n}{4}+\cdots+\binom{n}{2k}+\cdots$
negative_passages.docid: 100482
negative_passages.text: What's the formula for partitions where each group has a different size?
negative_passages.docid: 98941
negative_passages.text: Closed formula for the sums $\sum\limits_{1 \le i_1 < i_2 < \dots < i_k \le n} i_1 i_2 \cdots i_k $?