## Eigenvalues of Words in Two Positive Definite Letters

*Hillar, Christopher J*;

*Johnson, Charles R*;

- Subject: Mathematics - Operator Algebras | Mathematics - Rings and Algebras | 15A24, 15A57 | 15A18, 15A90arxiv: Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) | Computer Science::Formal Languages and Automata Theory

- References (6)
F (p, q) = F (p, q) = g1(q)ap + g2(q)bp + g3(q)cp, h1(p)rq + h2(p)sq + h3(p)tq, F (p, q) = F (p, q) = F (p, q) < 0; F (p, q) < 10 · F (p − 1, q); and F (p, q) < 10 · F (p, q − 1).

[BMV] D. Bessis, P. Moussa, and M. Villani, Monotonic converging variational approximations to the functional integrals in quantum statistical mechanics, J. Math. Phys., 16 (1975), pp. 2318-2325.

[HJ] R. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, New York, 1985.

[K] R. Kemp, On the number of words in the language {w ∈ Σ∗ | w = wR}2, Discrete Math., 40 (1982), pp. 225-234.

[S] I. Spitkovsky, private communication, Williamsburg, VA, 1999.

Mathematics Department, College of William and Mary, Williamsburg, VA 23187- 8795 E-mail address: crjohnso@math.wm.edu

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