arXiv subjects
Publications and source records attributed to S. Tarasov.
We compute generating functions of the set of directed lattice paths starting from the origin and avoiding a periodic set of even point on OX = "time"-axis. As an application we prove a combinatorial identity proposed by P. Hajnal and G.V. Nagy.
We settle the equivalence between the problem of hitting a polyhedral set by the orbit of a linear map and the intersection of a regular language and a language of permutations of binary words (the permutation filter realizability problem). The decidability of the both problems is presently unknown and the first one is a straightforward generalization of the famous Skolem problem and the nonnegativity problem in the theory of linear recurrent sequences. To show a `borderline' status of the permutation filter realizability problem with respect to computability we present some decidable and undecidable problems closely related to it.
We show that S.Vavasis' sufficient condition for global invertibility of a polynomial mapping can be easily generalized to the case of a general Lipschitz mapping. Keywords: Invertibility conditions, generalized Jacobian, nonsmooth analysis.
We present a simple geometric construction for smoothing polyhedral utility functions. Keywords: Afriat- Varian theorem, the utility function, the economic indices theory, convex analysis.