In this paper, the composition of Bhargava's cubes is generalized to the ring of integers of a number field of narrow class number one, excluding the case of totally imaginary number fields. The exclusion of the
Chalmers's exceptional composition: = A( φ 1) that φ 1 Importantly, Chalmers's mapping A is a bijection. So the structured proposition expressed by φ is recoverable from its mapping under A and vice-versa. From this perspective, Chalmers's proposal more closely resembles strategies denying ...
Let 7" be a translationally finite self-similar tiling of Rd. We prove that if 7" is nonperiodic, then it has the unique composition property. More generally, 7- has the unique composition property modulo the group of its translation symmetries. Introduction We consider tilings of the ...
If smp(G)=δ(G), then G is called maximally strong matched. 2. Preliminaries Let G1=(V1,E1), G2=(V2,E2), ⋯, Gk=(Vk,Ek) be k graphs, and let f1:V1→V2, f2:V2→V3, ⋯, fk−1:Vk−1→Vk, fk:Vk→V1 be k bijections. The k-composition networks G induced by ...
If |a | = 1, then ψ(u) = skc(u) for some nonzero constant s and . Let f be an analytic function on ; for any , denote (12) where fξ is called the slice function of f in ξ and fξ is an analytic function on . Now, we extend Lemma 5 to the case of in some ...
linear isometry T of a linear subspace A of L containing H onto such a subspace B, then T can be written as a weighted composition map, namely, Tf = ± (f o Sz) for all f A, where ± B, |±()| = 1 for all in the unit circle and S is an automorphism of L induced by ...
Finally, we consider a coloring problem equivalent to the characterization of such sequences for quasi-affine bijections. Niboucha, RazikaUSTHBSalinier, AlainUniv Limogesjournal de theorie des nombres de bordeaux
. ., f(k-1) : Vk-1 -> V-k, f(k) : V-k -> V-1 be k bijections. The k-composition networks G induced by G(1), G(2), . . ., G(k) is the graph with V (G) = U-k=1(k) V (G(t)) and E(G) = U-t=1(k) E(G(t)) boolean OR {(a(t), f(t)(a(r...
The enumeration of bicolored plane trees (A054357) has been significantly generalized in [2]. We note that (scaled) Shabat polynomials =-=[1, 4]-=- are also counted by A054357. 2 � •s2 Bijection The bijection from NC polygon diagrams to bicolored binary trees is depicted in the ...
We use these bijections to relate the multiplicity of a simple functor S H , V in M to the multiplicity of V in a certain K Out ( H )-module related to M ( H ). We then use these general results to study the structure of one of the important biset and related functors, namely...