50 citations · 124 across the 31 of their papers we have counts for
38 papers
On some integral properties of dimensions in Isaacs fusion categories
S. Burciu
For a fusion category, we prove some new integral properties concerning the dimension of a simple object that generates a Isaacs fusion subcategory. A stronger divisibility result…
Frobenius-Perron Dimensions of Conjugacy Classes and an Ito-Michler-Type Result in Modular Fusion Categories
S. Burciu
The influence of certain arithmetic conditions on the sizes of conjugacy classes of a finite group on the group structure has been extensively studied in recent years. In this pape…
On Harada's identity and some other consequences of Burnside's vanishing property
S. Burciu
In this short note, we prove some consequences of Burnside's vanishing property \cite{b-pa}. It is known that Harada's identity concerning the product of all conjugacy classes of a…
Burnside type results for fusion categories
Sebastian Burciu, Sebastien Palcoux
In this paper, we extend a classical vanishing result of Burnside from the character tables of finite groups to the character tables of commutative fusion rings, or more generally…
Structure constants, Isaacs property and Extended Haagerup fusion categories
Sebastian Burciu, Sebastien Palcoux
This paper presents an abstract Isaacs property that involves the Fourier transform for fusion rings, which may be non-commutative, thus expanding upon the commutative version desc…
On some Frobenius type divisibility results in a premodular category
Sebastian Burciu
In this note some new Frobenius type divisibility results are obtained for premodular categories. In particular, we extend Corollary 3.4 of [Yu20] from the settings of super-modula…