120 citations · 245 across the 69 of their papers we have counts for
72 papers
Matching algebras and their Dunkl subalgebras
Darij Grinberg, Anatol Kirillov, Boris Shapiro
For a finite simple graph , we consider the quotient algebra of the polynomial ring in the variables (for ) by the ideal generated by all…
Powers of matrices with all principal minors equal to 1
Darij Grinberg
We say that a square matrix is \emph{-principled} if all its principal minors are equal to . We show that over any well-behaved ring, any power of a -principled…
The V/L recursion for Macdonald's 7th Variation Schur polynomials
Darij Grinberg
We generalize and prove the recursive relation \[ S_λ(V) = \sum_{L\subseteq V\text{ line}} S_λ(V \mathbin{/\mkern-5mu/} L) \] conjectured by I. G. Macdonald for his "7th variation"…
Detropicalization as a proof technique
Darij Grinberg, Tom Roby
Rational functions make sense over any commutative ring, as long as the denominators are invertible. When there is no subtraction involved, they even apply over semirings (rings wi…
A constructive proof of Orzech's theorem
Darij Grinberg
Let be a commutative ring with unity, and a finitely generated -module. In 1971, Morris Orzech showed that any surjective -module homomorphism from a submodule of …
Compositions of -homomorphisms
Darij Grinberg
We study -homomorphisms in the sense of Khudaverdian--Voronov, but generalized to maps from arbitrary rings to arbitrary commutative rings. We show that the sum of an -homomo…