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Eulerian form of #2513: perturbed generalized Eulerian rows interlace - #2525
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strictInterl_cayleyTransform_succ_of_roots_mem_Icc: the Cayley transform preserves degree-raising interlacing of polynomials with roots in [-1, 0] (adjoin the root -1, which does not change the transform). strictInterl_C_mul_add_C_mul_one_add_X_pow_of_recurrence: for s >= 1 and c >= 1/2 the rows c E n + (1 - c) (1 + X)^n interlace strictly; the splits theorem becomes a corollary. orbitPerturbationRow_package now also records the degree. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Follow-up to #2524 (#2513, Eulerian form).
strictInterl_cayleyTransform_succ_of_roots_mem_Icc(inPolynomialValueEulerNumerator/Interlacing.lean): the Cayley transform preserves degree-raising interlacingp ≪ q,deg q = deg p + 1, for roots in[−1, 0]. The proof adjoins the root−1top(same degree-(n+1)transform) and reuses the same-degree theorem.strictInterl_C_mul_add_C_mul_one_add_X_pow_of_recurrence: fors ≥ 1,c ≥ 1/2,E 0 = 1andE (n+1) = (1 + (1 + s n) X) E n + s X (1 − X) E n', the rowsc E n + (1 − c)(1 + X)^ninterlace strictly; the splits theorem becomes a corollary.cayleyEulerOrbit_eq_generalizedEulerianandstrictInterl_C_mul_generalizedEulerian_add: theE naregeneralizedEulerian s n.orbitPerturbationRow_packagealso records the degree.Downstream: closes the
sorrysA141689_interlaces,A141689_prec,A141690_interlaces,A141690_precin real-rooted-oeis-proofs (PR to follow).Local checks: focused builds of touched modules and importers,
runLinter, catalog audit, proof status; axiomspropext,Classical.choice,Quot.sound.🤖 Generated with Claude Code