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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Positive definite matrices and Catalan numbers, revisited
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by Louis W. Shapiro PDF
Proc. Amer. Math. Soc. 90 (1984), 488-496 Request permission

Abstract:

In this note a combinatorial correspondence is used to prove that the number of positive definite, tridiagonal, integral matrices of determinant 1 whose sub and super diagonals consist solely of ones is ${C_n} = (_n^{2n})/(n + 1)$. The correspondence is then further used to count such matrices by trace and also by number of ones on the main diagonal. Other related correspondences and results are given including those for determinant equal to $2,3,4{\rm {and5}}$.
References
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 90 (1984), 488-496
  • MSC: Primary 05A15; Secondary 05C50
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0728375-5
  • MathSciNet review: 728375