= Markov interlacing lemma
{c}
{title2=$p\prec q\implies p^{(k)}\prec q^{(k)}$}
<Differentiation> preserves the ordering of <interlacing roots of polynomials> of equal or consecutive <polynomial degrees>. Iteration gives the result for every <derivative> for which both <polynomials> are nonconstant; common roots are allowed by a limiting argument. This is a result about the locations of <roots of a polynomial>, distinct from the <Markov inequality for polynomial derivatives>. Theorem A of https://www.math.bas.bg/mathmod/Proceedings_CTF/CTF-2010/files_CTF-2010/11-Dimitrov.pdf[Dimitar K. Dimitrov's account] states the first-derivative result.
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