Nekoliko kombinatornih dokaza
Abstract
Savremeni udzbenici kombinatorike i diskretne matematike isticu znacaj i eleganciju kombinatornih dokaza. U ovom radu navodimo nekoliko primjera kombinatornih dokaza koji se mogu mogu koristiti u nastavi. Na kraju dajemo kombinatorni dokaz Diksonovog identiteta pomocu puteva u cjelobrojnoj mrezi u prostoru.References
[1] A. C. Dixon, On the sum of the cubes of the coeficients in a certain expansion by the binomial theorem, Messenger of Mathematics, 20 (1891), pp. 79-80,
[2] V. J. W. Guo, A simple proof of Dixon's identity, Discrete Math., 268 (2003), pp. 309-310
[3] W. James, 100 years of Dixon's identity, Irish Mathematical Society Bulletin, 27 (1991), pp. 46-54,
[4] W. Koepf, Hypergeometric summation. An algorithmic approach to summation and special function identities, Springer, London, 2014
[5] R.P. Stanley, Enumerative combinatorics. Vol. 1. 2nd ed., Cambridge Studies in Advanced Mathematics, 49. Cambridge University Press, Cambridge, 2012.
[6] R.P. Stanley, Catalan Numbers, Cambridge, University Press, Cambridge, 2015.
[7] H. Wilf, generatingfunctionology, 2nd ed., Academic Press, Inc., Boston, 1994
[8] D. Zeilberger, Predavanje na Drzavnom univerzitetu u Sibiru, http://tube.sfu-kras.ru/video/396?playlist=397
[2] V. J. W. Guo, A simple proof of Dixon's identity, Discrete Math., 268 (2003), pp. 309-310
[3] W. James, 100 years of Dixon's identity, Irish Mathematical Society Bulletin, 27 (1991), pp. 46-54,
[4] W. Koepf, Hypergeometric summation. An algorithmic approach to summation and special function identities, Springer, London, 2014
[5] R.P. Stanley, Enumerative combinatorics. Vol. 1. 2nd ed., Cambridge Studies in Advanced Mathematics, 49. Cambridge University Press, Cambridge, 2012.
[6] R.P. Stanley, Catalan Numbers, Cambridge, University Press, Cambridge, 2015.
[7] H. Wilf, generatingfunctionology, 2nd ed., Academic Press, Inc., Boston, 1994
[8] D. Zeilberger, Predavanje na Drzavnom univerzitetu u Sibiru, http://tube.sfu-kras.ru/video/396?playlist=397
Published
2016-12-27
Issue
Section
Чланци