Dimension elevation formula for Chebyshevian blossoms

A given polynomial of degree less than or equal to n naturally “blossoms” into a function of n variables called its blossom. Considered as a polynomial function of degree less than or equal to (n+1) it “blossoms” into a “new” blossom which is now a function of (n+1) variables. A classical formula expresses any value of this new blossom as a strictly convex combination of (n+1) values of the initial one. We establish a similar formula for Chebyshevian blossoms.