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We study the tomographic clustering properties of the photometric clustercatalogue derived from the Third Data Release of the Kilo Degree Survey,focusing on the angular correlation function and its spherical harmoniccounterpart, the angular power spectrum. We measure the angular correlationfunction and power spectrum from a sample of 5162 clusters, with an intrinsicrichness $\lambda^*\geq 15$, in the photometric redshift range $z\in [0.1,0.6]$, comparing our measurements with theoretical models, in the framework ofthe $\Lambda$-Cold Dark Matter cosmology. We perform a Monte Carlo Markov Chainanalysis to constrain the cosmological parameters $\Omega_{\mathrm{m}}$,$\sigma_8$ and the structure growth parameter $S_8\equiv\sigma_8\sqrt{\Omega_{\mathrm{m}}/0.3}$. We adopt Gaussian priors on the parameters ofthe mass-richness relation, based on the posterior distributions derived from aprevious joint analysis of cluster counts and weak lensing mass measurementscarried out with the same catalogue. From the angular correlation function, weobtain $\Omega_{\mathrm{m}}=0.32^{+0.05}_{-0.04}$,$\sigma_8=0.77^{+0.13}_{-0.09}$ and $S_8=0.80^{+0.08}_{-0.06}$, in agreement,within $1\sigma$, with 3D clustering result based on the same cluster sampleand with existing complementary studies on other datasets. For the angularpower spectrum, we derive statistically consistent results, in particular$\Omega_{\mathrm{m}}=0.24^{+0.05}_{-0.04}$ and $S_8=0.93^{+0.11}_{-0.12}$,while the constraint on $\sigma_8$ alone is weaker with respect to the oneprovided by the angular correlation function, $\sigma_8=1.01^{+0.25}_{-0.17}$.Our results show that the 2D clustering from photometric cluster surveys canprovide competitive cosmological constraints with respect to the full 3Dclustering statistics, and can be successfully applied to ongoing andforthcoming spectro/photometric surveys.

AMICO galaxy clusters in KiDS-DR3: Cosmological constraints from angular power spectrum and correlation function