We generalize a map by S. Mason regarding two combinatorial models for key polynomials, in a way that accounts for the major index. Furthermore we define a similar variant of this map, that regards alternative models for the modified Macdonald polynomials at t = 0, and thus partially answers a question by J. Haglund. These maps together imply a certain uniqueness property regarding inversion– a...

Abstract: In this paper, we study ZpZp[u]-additive codes, where p is prime and u 2 = 0. In particular, we determine a Gray map from ZpZp[u] to Z α+2β p and study generator and parity check matrices for these codes. We prove that a Gray map Φ is a distance preserving map from (ZpZp[u],Gray distance) to (Z α+2β p ,Hamming distance), it is a weight preserving map as well. Furthermore we study the ...