100 citations · 291 across the 51 of their papers we have counts for
62 papers
Classifying integral Grothendieck rings up to rank 5 and beyond
Max A. Alekseyev, Winfried Bruns, Jingcheng Dong +1
In this paper, we define a Grothendieck ring as a fusion ring categorifiable into a fusion category over the complex field. An integral fusion ring is called Drinfeld if all its fo…
-graded rings and their canonical modules
Margherita Barile, Winfried Bruns
In ``Cohen--Macaulay rings'' Bruns and Herzog define the graded canonical module for -graded rings. We generalize the definition to multigradings and prove that the c…
Sagbi bases, defining ideals and algebra of minors
Winfried Bruns, Aldo Conca, Francesca Lembo
This paper extends the article of the Bruns and Conca on SAGBI bases and their computation (J. Symb. Comput. 120 (2024)) in two directions. (i) We describe the extension of the Sin…
A New Invariant of Lattice polytopes
Winfried Bruns, Takayuki Hibi
The maximal degree of monomials belonging to the unique minimal system of monomial generators of the canonical module of the toric ring defin…
Sagbi combinatorics of maximal minors and a Sagbi algorithm
Winfried Bruns, Aldo Conca
The maximal minors of a matrix of indeterminates are a universal Gröbner basis by a theorem of Bernstein, Sturmfels and Zelevinsky. On the other hand it is known that they are not…
Classification of integral modular data up to rank 13
Max A. Alekseyev, Winfried Bruns, Sebastien Palcoux +1
This paper classifies the modular data of integral modular fusion categories up to rank 13, and integral half-Frobenius fusion rings up to rank 12. We establish that every perfect…