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math.RA2026
The prime spectrum of the talented monoid of a higher-rank graph and applications
Roozbeh Hazrat, Promit Mukherjee
In this paper, we further investigate the role of the graded Grothendieck group $K_0^{\gr}$ and its positive cone (the talented monoid) as an effective tool for distinguishing stru…
math.RA2026
Some more talents of the talented monoid of a higher-rank graph
Roozbeh Hazrat, Huanhuan Li, Promit Mukherjee
In this paper, we explore the idea that the graded Grothendieck group , or equivalently its positive cone, the talented monoid, can detect the structural type of higher-r…
math.DS2026
Higher-Dimensional Symbolic Dynamics: A Textile Framework For 3-graphs
Roozbeh Hazrat, Promit Mukherjee, Sujit Kumar Sardar
Textile systems are best known to model two-dimensional shifts of finite type. In this article, we associate a discrete algebra with a textile system and provide a groupoid model f…