#### Filter Results:

#### Publication Year

1982

2010

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

Shapiro, L.

- Wen-Jin Woan, Ldszlo Szalay, Chu Wenchang, Paul Thomas Young, Thomas Koshy, Napoleon Gauthier +4 others
- 1999

0. INTRODUCTION For a natural number vand two sequences {A(k),B(k)} k of binomial coefficients, the following convolutions of Vandermonde type, C(rn, w, v): = ]T A(m + kv)B{n-kv) , k will be investigated in this paper. When v = 2, 3, 4, the convolutions will be nominated duplicate, triplicate, and quadruplicate, respectively. Thanks to the explicit… (More)

- Paul Peart, Wen-Jin Woan
- 2000

When the Hankel matrix formed from the sequence 1, a 1 , a 2 , ... has an LDL T decomposition, we provide a constructive proof that the Stieltjes matrix S L associated with L is tridiagonal. In the important case when L is a Riordan matrix using ordinary or exponential generating functions, we determine the specific form that S L must have, and we… (More)

- Wen-Jin Woan
- 2001

A Dyck path of length 2n is a path in two-space from (0, 0) to (2n, 0) which uses only steps (1, 1) (northeast) and (1, −1) (southeast). Further, a Dyck path does not go below the x-axis. A peak on a Dyck path is a node that is immediately preceded by a northeast step and immediately followed by a southeast step. A peak is at height k if its y-coordinate is… (More)

- Wen-jin Woan
- 2001

Let H be the Hankel matrix formed from a sequence of real numbers S = {a 0 = 1, a 1 , a 2 , a 3 , ...}, and let L denote the lower triangular matrix obtained from the Gaussian column reduction of H. This paper gives a matrix-theoretic proof that the associated Stieltjes matrix S L is a tri-diagonal matrix. It is also shown that for any sequence (of nonzero… (More)

- Wen-jin Woan
- 2006

We consider those lattice paths that use the steps " up " , " level " , and " down " with assigned weights w, b, c. In probability theory, the total weight is 1. In combinatorics, we replace weight by the number of colors. Here we give a combinatorial proof of a relation between restricted and unrestricted weighted Motzkin paths.

Most of people knows the following problem, What is the next term ? What expression would give us the general term ? It would be nice to have a formula to generate all the terms in the sequence. how do we find the formula? here is the way to become a 'genius' at MENSA tests.