Generalized Vandermonde Matrices with Missing Row-Powers

Let . Let with distinc s. Let be a set of distinct nonnegative row-powers. Consider the Generalized Vandermonde matrix . When , this matrix becomes the ordinary Vandermonde matrix, .

An equivalent description of is the largest row-power and the set of missing rows from : that is, the items that are in  but not in . Let be this set. Define the punctured Generalized Vandermonde matrix . Let be the th elementary symmetric polynomial.

Now we are ready to present some interesting results without proof, from the paper “Lower bound on Sequence Complexity” by Kolokotronis, Limniotis, and Kalouptsidis.

I will add some applications later on.

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