120 citations · 245 across the 69 of their papers we have counts for
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The trace Cayley-Hamilton theorem
Darij Grinberg
In this expository paper, various properties of matrix traces, determinants and adjugate matrices are proved, including the *trace Cayley-Hamilton theorem*, which says that \[ kc_k…
Top to random and reverse: analysis of a new descent algebra shuffle
Darij Grinberg, Jonathan Parlett
We study the "top-to-random-and-reverse shuffle", defined as the top-to-random shuffle in the symmetric group algebra composed with the permutation (which sends each to $…
The representation theory of somewhere-to-below shuffles
Darij Grinberg
The *somewhere-to-below shuffles* are the elements \[ t_{\ell} := \operatorname{cyc}_{\ell}+\operatorname{cyc}_{\ell,\ell+1}+\operatorname{cyc}_{\ell,\ell+1,\ell+2}+\cdots+\operato…
An introduction to the algebra of rings and fields
Darij Grinberg
This is an introduction to rings and fields, written for a quarter-long undergraduate course. It includes the basic properties of ideals, modules, algebras and polynomials, the con…
Rook sums in the symmetric group algebra
Darij Grinberg
Let be the group algebra of the -th symmetric group over a commutative ring . For any two subsets and of , we defi…
An introduction to the symmetric group algebra
Darij Grinberg
This is an introduction to the group algebras of the symmetric groups, written for a quarter-long graduate course. After recalling the definition of group algebras (and monoid alge…