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Let I₍, ₌ = (x₁ x₌, x₂ x₌+₁, , x₍+₁x₍+₂ x₍+₌) be the m-path ideal of a path of length n + m-1 over a polynomial ring S = kx₁, , x₍+₌. We compute all the graded Betti numbers of all powers of I₍, ₌.
Bălănescu et al. (Tue,) studied this question.