EULERIAN STRATIFICATION OF POLYHEDRA

In this paper we introduce Eulerian stratifications, weight functions, and boundary weight functions to study linear conditions on f-vectors of stratified triangulations on arbitrary polyhedra. The Eulerian str atified spaces are characterized by the Euler characteristics of the l inks between strata. With the new concepts, the classical Dehn-Sommerv ille equations are generalized to weighted f-vectors of arbitrary poly hedra; and the linear conditions on weighted f-vectors of all stratifi ed triangulations are classified. Moreover, the necessary and sufficie nt conditions are obtained for given numbers to be the Euler character istics of the links between strata, and a procedure of constructing Eu lerian stratifications from the given numbers on posets is provided. O ur study of Eulerian stratifications and weight functions suggests tha t the underlying combinatorial information should become a rather gene ral setup that includes many classical linear combinatorial theories. It also points out a possible approach toward the study on f-vectors o f triangulations of more general spaces. (C) 1998 Academic Press.