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3
questions
5
votes
1
answer
215
views
Series of polynomials very nearly follows binomial coefficients but doesn't quite
I'm modelling a system using a Markov chain and by a few iterations of the transition matrix I can see a pattern emerging in the resulting polynomial that really looks like Pascal's triangle, but isn'...
- 53
15
votes
5
answers
4k
views
Inverse of the Pascal Matrix
Let $P_n$ be the $(n+1) \times (n+1)$ matrix that contains the numbers of Pascal's triangle in the upper triangle. For example in the case of $n=3$
$$
P_3 =
\begin{pmatrix}
1 & 1 & 1 & 1 \...
- 3,123
4
votes
3
answers
549
views
matrix representations and polynomials
I just investigated the following matrix and some of its lower powers:
$${\bf M} = \left[\begin{array}{cccc}
1&0&0&0\\
1&1&0&0\\
1&1&1&0\\
1&1&1&1
\end{...
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