A Famous Identity of Hajós in Terms of Sets Rui Duarte
Center for Research and Development in Mathematics and Applications
Department of Mathematics
University of Aveiro
3810-193 Aveiro
Portugal
mailto:rduarte@ua.ptrduarte@ua.pt

António Guedes de Oliveira
CMUP and Mathematics Department
Faculty of Sciences
University of Porto
4099-002 Porto
Portugal
mailto:agoliv@fc.up.ptagoliv@fc.up.pt

in

Abstract:

By considering the famous identity on the convolution of the central binomial coefficients

$$\sum_{i+j=n} {{2i} \choose i} {{2j} \choose j} = 4^n$$

in terms of pairs of $\ell$-subsets of $2\ell$-sets, we obtain a new bijective proof and new identities that can be seen as refinements.