By the pioneering work of Huckster and Richard Stanley it has become evident that there are strong interactions between Commutative Algebra and Combinatory. On one hand side the theory of monomial ideals, mitigated modules and tonic rings is studied with techniques from Combinatory (simplified complexes, sellable posits, integral palmtop theory) while on the other hand Hilbert functions, resolutions, Rees algebras and homological properties if ideals and their powers can often be studied using Groaner and Samba basis reducing the problem to similar problem on monomial ideals or tonic rings where combinatorial technique are available. The intended scientific cooperation shall enable us to continue our research in the study of classes of monomial ideals, resolutions and homological invariants of graded ideals and modules.
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