Mathematics > Home > Advances in Pure and Applied Mathematics > Issue 2 (March 2025) > Article
Edoardo Ballico
University of Trento
Italy
Published on 20 March 2025 DOI : 10.21494/ISTE.OP.2025.1259
Let be a degree form in variables . Any additive decomposition of is associated to a finite set with the number of non-proportional addenda. We study the index of regularity of , i.e. the first integer such that , of the finite subset associated to the additive decompositions of degree forms in variables. Obviously . We prove that if spans and is the maximal integer such that divides at least one monomial of . If essentially depends on less variables, but spans , then . We give examples (but with bigger that the rank of ) in which we have .
Let be a degree form in variables . Any additive decomposition of is associated to a finite set with the number of non-proportional addenda. We study the index of regularity of , i.e. the first integer such that , of the finite subset associated to the additive decompositions of degree forms in variables. Obviously . We prove that if spans and is the maximal integer such that divides at least one monomial of . If essentially depends on less variables, but spans , then . We give examples (but with bigger that the rank of ) in which we have .