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Results tagged with matrices
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user 48831
Questions where the notion matrix has an important or crucial role (for the latter, note the tag matrix-theory for potential use). Matrices appear in various parts of mathematics, and this tag is typically combined with other tags to make the general subject clear, such as an appropriate top-level tag ra.rings-and-algebras, co.combinatorics, etc. and other tags that might be applicable. There are also several more specialized tags concerning matrices.
7
votes
Eigenvalues of a matrix with entries involving combinatorics
These matrices are subject of the fascinating article Carries, Combinatorics and an Amazing Matrix by John Holte
(American Mathematical Monthly, 104 (2), 1997)). … They are the transition matrices for the Markov chains describing the
descents in the permutations generated by shuffling a deck of $n$ cards with successive $b$-shuffles. …
- 3,255
5
votes
Accepted
Result attribution for eigenvalues of a matrix of Pascal-type
I don't know a reference. One way to show the eigenvalues starts from the observation (which can be proved using
generating functions)
that $\sum_{i=0}^n {i\choose k} A_{i,j}={2n+1 \choose n-k} {j+k …
- 3,255