The i-th Betti number of configuration spaces of 'bunch of grapes' graphs is exactly a polynomial in k for all k, given by a convolution of local first Betti polynomials.
Configuration spaces and braid groups of graphs
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Hilbert polynomials of configuration spaces over graphs of circumference at most 1
The i-th Betti number of configuration spaces of 'bunch of grapes' graphs is exactly a polynomial in k for all k, given by a convolution of local first Betti polynomials.