Elementary symmetric polynomials in Shamir's scheme (Q984842)

Building on two papers of A. Schinzel, S. Spież, J. Urbanowicz [Finite Fields Appl. 16, No. 6, 449--462 (2010; Zbl 1209.94054)] and S. Spież, M. Srebrny, J. Urbanowicz (yet unpublished), the paper characterizes when the track \((1,2,\dots,n)\) is \(k\)-admissible over the field \(\mathbb F_p\). The result implies that almost always this is the case, when \(n\) is the number of shareholders and \(k\) is the threshold in Shamir's secret sharing scheme.