In order to analyse the US-Iran relations, the RSCT
is modified as both these countries are not geographically proximate and have common security challenges till the emergence of 'Islamic State.' However, the US presence in Iraq, Afghanistan and its naval fleet in the Persian Gulf makes it proximate to the Middle Eastern regional security complex (RSC), where Iran as an important regional actor is swaying influence from Iraq to Sudan.
Also, a RSCT F with n cells is standard if [x.sup.F] = [PI].sup.n.sub.i=1] [x.sub.i].
Then the row-strict quasisymmetric Schur function [RS.sub.[alpha]] is given by [RS.sub.[alpha]] = [[summation].sub.T] [x.sup.T], where the sum is over all RSCT's T of shape [alpha].
The following map sends a reverse row-strict tableau T to a RSCT [rho](T) = F.
Lemma 3.2 The map [rho] is a weight preserving bijection between the set of reverse row-strict tableaux of shape [lambda] and the set of RSCT's of shape a where [lambda]([alpha]) = [lambda].
The following analogue of dual Schensted insertion provides a method for inserting a new cell into a RSCT. Given an arbitrary RSCT F, let read(F) be the reading word for F given by reading the entries of F by column from right to left, reading the columns from top to bottom.
Lemma 6.1 The insertion procedure F [??] x produces an RSCT.