10 Total number of integers relatively prime to $p^2$ 6 Problem from a graph theory book 5 How to prove $\sum_{k=3}^n \binom nk \binom k3 =\binom n3 2^{n-3}$ 5 How can I prove $R^T\ ;R^T$ is transitive if $R$ is transitive. 4 How many $4$ digit numbers can be made with exactly $3$ digits the same?

Reputation (3,576)

 +5 Set builder notation: Colon or Vertical Line +10 Proof that $\sum_k (-1)^k \binom{n-k}{n-m} \binom{m}{k} = \binom{n-m}{m}$ +10 Total number of integers relatively prime to $p^2$ +10 Terminology for sets which are permuted within themselves on repeated application of a function

Questions (13)

 25 Set builder notation: Colon or Vertical Line 20 Average distance from center of circle 2 Confusion on “Lyndon Words, Free Algebras, and Shuffles” 2 Decomposition into Lyndon Words 2 A set is compact iff all closed collections of subsets with the f.i.p. have nonempty intersection

Tags (103)

 72 combinatorics × 62 18 group-theory × 15 29 discrete-mathematics × 33 17 elementary-number-theory × 11 26 abstract-algebra × 20 15 elementary-set-theory × 13 21 probability × 22 14 relations × 10 21 permutations × 22 14 graph-theory × 8

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 Mathematics 3,576 rep 21531 History of Science and Mathematics 378 rep 27 Literature 144 rep 4 MathOverflow 101 rep 2 Mathematics Educators 101 rep 1