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arxiv: math/0502348 · v1 · submitted 2005-02-16 · 🧮 math.AC · math.CO

Computation of Poincare-Betti series for monomial rings

classification 🧮 math.AC math.CO
keywords monomialcharacteristicfieldgeneratorsgivenpoincare-bettipolynomialseries
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The multigraded Poincare-Betti series P_R^k(x_1,...,x_n; t) of a monomial ring k[x_1,...,x_n]/<M> on a finite number of monomial generators has the form (1+tx_1)(1+tx_2)...(1+tx_n)/b_(R,k)(x_1,...,x_n; t), where b_(R,k)(x_1,...,x_n;t) is a polynomial depending only on the monomial set M and the characteristic of the field k. I present a computer program designed to calculate the polynomial b_(R,k) for a given field characteristic and a given set of monomial generators.

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