Adding a suitable extra point E to P_n(x) produces complete zero interlacing with G_k when the polynomials obey appropriate mixed recurrence relations.
A unified approach to polynomial sequences with only real zeros
2 Pith papers cite this work. Polarity classification is still indexing.
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Derives generating functions for rectangle tilings with Ferrers tiles, proves real-rootedness and interlacing of independence polynomials, links results to OEIS sequences, and shows the two-column case yields real-rooted interlacing sequences.
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Separating zeros of polynomials using an added interlacing point
Adding a suitable extra point E to P_n(x) produces complete zero interlacing with G_k when the polynomials obey appropriate mixed recurrence relations.
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Polynomials from tilings of rectangles
Derives generating functions for rectangle tilings with Ferrers tiles, proves real-rootedness and interlacing of independence polynomials, links results to OEIS sequences, and shows the two-column case yields real-rooted interlacing sequences.