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Families

• Family≔ 2 definitions⊢ 4 theoremsEulerian polynomialsMain results: Eulerian polynomials are real-rooted; Type B Eulerian polynomials are real-rootedFrobenius & Brenti · 1910–1994→
• Family≔ 1 definition⊢ 6 theoremsGeneralized Laguerre polynomialsMain results: Generalized Laguerre polynomials are real-rooted→
• Family≔ 2 definitions⊢ 3 theoremsGeneralized Narayana polynomialsMain results: Generalized Narayana polynomials are real-rooted; The Narayana transform preserves Pólya-frequency polynomialsMao, Wang, Dominici, Johnston & Jordaan · 2013–2026→
• Family≔ 5 definitions⊢ 9 theoremsGeneralized snake posetsMain results: Braun–Jal, Theorem 3.5: the snake recurrence; Braun–Jal, Theorem 4.1: snake polynomials are real-rooted and interlaceBraun & Jal · 2026→
• Family≔ 2 definitions⊢ 6 theoremsHermite polynomialsMain results: Hermite polynomials are real-rooted→
• Family≔ 4 definitions⊢ 5 theoremsParking functionsMain results: Parking function descent polynomials are real-rooted; Tieless parking function descent polynomials are real-rooted; …→