Institute Output

An Invitation to Higher Arity Science
Carlos Zapata-Carratalá, Xerxes D. Arsiwalla
Exploration of a wide range of higher-order phenomena across multiple disciplines and the preliminary application of hypergraph and hypermatrix methods.

Biunit pairs in semiheaps and associated semigroups
Bernard Rybołowicz, Carlos Zapata-Carratalá
This research introduces biunit pairs in semiheaps, and establishes a direct correspondence between monoids with specific switches and semiheaps, leading to the novel concept of diheaps.

Hypermatrix Algebra and Irreducible Arity in Higher-Order Systems: Concepts and Perspectives
Carlos Zapata-Carratalá, Maximilian Schich, Taliesin Beynon, Xerxes D. Arsiwalla
Hypergraph and hypermatrix methods are applied to detect irreducible interactions in higher-order systems.

Diagrammatic calculus and generalized associativity for higher-arity tensor operations
Carlos Zapata-Carratalá, Xerxes D. Arsiwalla, Taliesin Beynon