Invariant and geometric aspects of algebraic complexity theory. I (Q1176389)

The author investigates the following problem: What is the minimum number, denoted by \(L_ +(v_ 1,v_ 2,\dots,v_ t\mid x_ 1,x_ 2,\dots,x_ n)\), of those additive steps required to compute a given set \(v=(v_ 1,\dots,v_ t)\) of \(t\) linear forms of variables \(x_ 1,x_ 2,\dots,x_ n\). He establishes a natural connection of this question with some problems of graph theory, projective geometry, algebraic geometry and recent results in application of combinatorics to classical invariant theory [cf. \textit{P. Doubilet}, \textit{G. C. Rota} and \textit{J. Stein}, Stud. Appl. Math. 53, 185-216 (1974; Zbl 0426.05009)]. There are elementary motive examples in the paper. In the following paper the author intends to consider some interesting questions arisen in his investigations in this field.