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Double counting (proof technique)
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==References== *{{citation | last1 = Aigner| first1 = Martin | last2 = Ziegler| first2 = Günter M.| author2-link = Günter M. Ziegler | publisher = Springer-Verlag | title = [[Proofs from THE BOOK]] | year = 1998}}. Double counting is described as a general principle on page 126; Pitman's double counting proof of Cayley's formula is on pp. 145–146; Katona's double counting inequality for the Erdős–Ko–Rado theorem is pp. 214–215. *{{citation | last = Euler| first = L. | journal = Commentarii Academiae Scientiarum Imperialis Petropolitanae | pages = 128–140 | title = Solutio problematis ad geometriam situs pertinentis | url = http://math.dartmouth.edu/~euler/docs/originals/E053.pdf | volume = 8 | year = 1736}}. Reprinted and translated in {{citation | last1 = Biggs| first1 = N. L. | last2 = Lloyd| first2 = E. K. | last3 = Wilson| first3 = R. J. | publisher = Oxford University Press | title = Graph Theory 1736–1936|title-link=Graph Theory, 1736–1936 | year = 1976}}. *{{citation | doi = 10.2307/3219324 | last1 = Garbano| first1 = M. L. | last2 = Malerba| first2 = J. F. | last3 = Lewinter| first3 = M. | journal = Mathematics Magazine | jstor = 3219324 | pages = 216–217 | title = Hypercubes and Pascal's triangle: a tale of two proofs | issue = 3 | volume = 76 | year = 2003}}. *{{citation | last = Joshi | first = Mark | contribution = Double Counting | doi = 10.1007/978-3-319-16250-8_2 | pages = 11–17 | publisher = Springer International Publishing | title = Proof Patterns | year = 2015| isbn = 978-3-319-16249-2 }} *{{citation | last = Klavžar| first = Sandi | doi = 10.1016/j.disc.2005.10.036 | issue = 22 | journal = [[Discrete Mathematics (journal)|Discrete Mathematics]] | pages = 2964–2967 | title = Counting hypercubes in hypercubes | volume = 306 | year = 2006| doi-access = free }}. *{{citation | last1 = van Lint| first1 = Jacobus H. | last2 = Wilson| first2 = Richard M. | title = A Course in Combinatorics | page = 4 | publisher = Cambridge University Press | year = 2001 | isbn = 978-0-521-00601-9}}. [[Category:Enumerative combinatorics]] [[Category:Articles containing proofs]] [[Category:Mathematical proofs]]
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