NONREALIZABILITY OF CERTAIN REPRESENTATIONS IN FUSION SYSTEMS

On Properties of Representations in Certain Linear Numeration Systems

Given a ≥ b, let G0 = 1, G1 = a+ 1, and Gn+2 = aGn+1 + bGn for n ≥ 0. For each choice of a and b, we have a linear recurrence that defines a numeration system. Every positive integer n may be written as the sum of the Gn, with alphabet A = {0, 1, . . . a}, in one or more different ways. Let R(a,b)(n) be the function that counts the number of distinct representations of an integer as a sum of th...

compactifications and representations of transformation semigroups

this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...

On Certain Analytical Representations of Cellular Automata

The last decades, the field of Cellular Automata (CA) had a rapid expansion after its initial revival with the seminal Wolfram’s paper [1] both due to the increase of computational power allowing exploration of large configurations in sufficient time depth as well as the meeting with other fields like Machine Learning (ML) and Artificial Intelligence (AI) [2], [3], [4] where it delivered promis...

On the Signature of Certain Spherical Representations

Let G be a real semisimple Lie group. Let g0 be the Lie algebra of G. We will denote the complexification of any vector space V0 by V and its dual by V ∗. Let g0 = k0 + p0 be a fixed Cartan decomposition corresponding to the Cartan involution θ of g0. Let K be the corresponding maximal compact subgroup of G. Let us fix T ⊂ K a maximal torus. Define S ⊂ t∗ as the set of weights of T that are sum...

Representations of certain isotropic tensor functions