The Combinatorics of Flag Enumeration, Permutations and Material Science

We propose to study the flag ¯ f-vector of Whitney stratified spaces and to find linear inequalities for the flag ¯ f-vector. This work is motivated by classical polytopal theory. The research will use the cd-index, a non-commutative polynomial which in effect provides the minimal basis to view the flag data. The work is based upon ideas arising from a new results of the PI, Goresky and Readdy [10].