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- LOUIS W. SHAPIRO
- 2010

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 " = (2 " ")/(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… (More)

- Louis W. Shapiro, Seyoum Getu, Wen-Jin Woan, Leon C. Woodson
- Discrete Applied Mathematics
- 1991

Shapiro, L.

- Emeric Deutsch, Louis W. Shapiro
- Discrete Mathematics
- 2001

- Robert Donaghey, Louis W. Shapiro
- J. Comb. Theory, Ser. A
- 1977

- Emeric Deutsch, Louis W. Shapiro
- Discrete Mathematics
- 2002

- Louis W. Shapiro, A. B. Stephens
- SIAM J. Discrete Math.
- 1991

- Gi-Sang Cheon, Louis W. Shapiro
- Appl. Math. Lett.
- 2008

- Louis W. Shapiro
- J. Comb. Theory, Ser. A
- 1976

- William Y. C. Chen, Nelson Y. Li, Louis W. Shapiro
- Discrete Applied Mathematics
- 2007

We introduce the notion of doubly rooted plane trees and give a decomposition of these trees, called the butterfly decomposition which turns out to have many applications. From the butterfly decomposition we obtain a one-to-one correspondence between doubly rooted plane trees and free Dyck paths, which implies a simple derivation of a relation between the… (More)

- William Y. C. Chen, Nelson Y. Li, Louis W. Shapiro, Sherry H. F. Yan
- Eur. J. Comb.
- 2007

We give a combinatorial interpretation of a matrix identity on Catalan numbers and the sequence (1, 4, 4 2 , 4 3 ,. . .) which has been derived by Shapiro, Woan and Getu by using Riordan arrays. By giving a bijection between weighted partial Motzkin paths with an elevation line and weighted free Motzkin paths, we find a matrix identity on the number of… (More)