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Theorems

Theorem 1 definition 2 theoremsAissen–Schoenberg–WhitneyAissen, Schoenberg & Whitney · 1952
Theorem 4 definitions 3 theoremsBorcea–Brändén finite-symbol theoremsBorcea & Brändén · 2009
Theorem 1 definition 1 theoremBrändén–Solus symmetric decompositionBrändén & Solus · 2019
Theorem 2 theoremsCauchy interlacingFisk · 2005
Theorem 4 definitions 8 theoremsChow polynomials of totally nonnegative matricesBrändén & Vecchi · 2025
Theorem 2 definitions 1 theoremClaw-free independence polynomialsChudnovsky & Seymour · 2007
Theorem 2 definitions 2 theoremsDescartes' rule of signsDescartes · 1637
Theorem 1 definition 2 theoremsFavard recurrencesFavard · 1935
Theorem 5 definitions 8 theoremsHadamard products and Schur–Szegő compositionMaló, Pólya, Schur, Wagner & Garloff · 1895–1996
Theorem 3 theoremsHermite–Biehler and Hurwitz criteriaHoltz · 2003
Theorem 1 definition 1 theoremHermite–Poulain theoremHermite & Poulain
Theorem 1 definition 1 theoremInterlacing from a monomial chain
Theorem 2 definitions 1 theoremKurtz’s coefficient criterionKurtz · 1992
Theorem 4 definitions 5 theoremsLindström–Gessel–Viennot and total positivityLindström, Gessel & Viennot · 1973–1985
Theorem 3 definitions 4 theoremsLiu's opposite-sign compatibility theoremLiu · 2012
Theorem 3 definitions 2 theoremsMatrices preserving interlacing sequencesFisk & Brändén · 2006–2015
Theorem 2 definitions 3 theoremsObreschkoff’s theoremObreschkoff & Dedieu · 1963–1992
Theorem 2 definitions 1 theoremOperators preserving interlacingBrändén · 2011
Theorem 1 definition 5 theoremsPerron–Frobenius theoremPerron & Frobenius · 1907–1912
Theorem 3 definitions 6 theoremsReal-rooted Eulerian variationsAlexandersson · 2026
Theorem 3 definitions 4 theoremsRook polynomialsNijenhuis · 1976
Theorem 3 definitions 3 theoremsSame-phase stability for graph polynomialsLeake & Ryder · 2019
Theorem 3 definitions 2 theoremsSturm root countingSturm · 1829
Theorem 2 definitions 8 theoremsThe binary-run transformation
Theorem 2 definitions 3 theoremsToric g-contribution polynomialsXiao · 2026
Theorem 4 definitions 11 theoremsTotally nonnegative matrices and chain polynomialsBrändén & Saud Leite · 2024
Theorem 1 definition 1 theoremVeronese sections
Theorem 3 theoremsWagner’s lemmaWagner · 1992