On the \(H\)-polynomial of certain monomial curves (Q1880983)

Let \(0<m_0<m_1<\dots<m_{e-1},\) \(\gcd(m_0,\dots,m_{e-1})=1\) be integers such that \(m_0,\dots,m_{e-2}\) is an arithmetic sequence and \(m_{e-1}\) is arbitrary. Let us consider the coordinate ring \(A\) of the algebroid monomial curve in the affine \(e\)-space over a field \(K,\) defined parametrically by \(X_0=T^{m_0},\dots,X_{e-1}=T^{m_{e-1}}\) (in particular these hypotheses say that the associated graded ring of \(A\) is Cohen-Macaulay). Under some additional assumptions the authors give an algorithmic method to write down the \(h\)-polynomial of \(A\) explicitly (so they also determine the Hilbert function of \(A\)).