For monomial ideals in K[x,y] with reduction ideal (x^a, y^b), the paper provides explicit upper bounds, complete classifications for reduction numbers 1 and g-1, exact formulas for 3-generated ideals, and results on reduction numbers of powers.
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On the monomial reduction number of a monomial ideal in $K[x,y]$
For monomial ideals in K[x,y] with reduction ideal (x^a, y^b), the paper provides explicit upper bounds, complete classifications for reduction numbers 1 and g-1, exact formulas for 3-generated ideals, and results on reduction numbers of powers.