Related papers: Group Actions and Some Combinatorics on Words with…
We investigate the average-case complexity of decision problems for finitely generated groups, in particular the word and membership problems. Using our recent results on ``generic-case complexity'' we show that if a finitely generated…
We introduce an algebraic structure for studying state-independent contextuality arguments, a key form of quantum non-classicality exemplified by the well-known Peres-Mermin magic square, and used as a source of quantum advantage. We…
For symplectic group actions which are not Hamiltonian there are two ways to define reduction. Firstly using the cylinder-valued momentum map and secondly lifting the action to any Hamiltonian cover (such as the universal cover), and then…
The computational complexity of time-dependent perturbation theory is well-known to be largely combinatorial whatever the chosen expansion method and family of parameters (combinatorial sequences, Goldstone and other Feynman-type…
From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing…
We generalize certain totient functions using elementary symmetric polynomials and derive explicit product forms for the totient functions involving the second elementary symmetric sum. This work follows from the work of Toth [The Ramanujan…
We propose a universal group theoretic description of the fermion production through any type of interaction to scalar or pseudo-scalar. Our group theoretic approach relies on the group $SU(2) \times U(1)$, corresponding to the freedom in…
An associative $*$-algebra is introduced (containing a $TTR$-algebra as a subalgebra) that implements the form factor axioms, and hence indirectly the Wightman axioms, in the following sense: Each $T$-invariant linear functional over the…
These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…
We formulate a complex action theory which includes operators of coordinate and momentum $\hat{q}$ and $\hat{p}$ being replaced with non-hermitian operators $\hat{q}_{new}$ and $\hat{p}_{new}$, and their eigenstates ${}_m <_{new} q |$ and…
Let A be an abelian surface over F_q, the field of q elements. The rational points on A/\F_q form an abelian group A(\F_q) \simeq \Z/n_1\Z \times \Z/n_1 n_2 \Z \times \Z/n_1 n_2 n_3\Z \times\Z/n_1 n_2 n_3 n_4\Z. We are interested in knowing…
We study and classify free actions of compact quantum groups on unital C*-algebras in terms of generalized factor systems. Moreover, we use these factor systems to show that all finite coverings of irrational rotation C*-algebras are cleft.
We present a new approach to the proof of ergodic theorems for actions of free groups based on geometric covering and asymptotic invariance arguments. Our approach can be viewed as a direct generalization of the classical geometric covering…
We define the notion of a partial action on a generalized Boolean algebra and associate to every such system and commutative unital ring $R$ an $R$-algebra. We prove that every strongly $E^{\ast}$-unitary inverse semigroup has an associated…
By applying the property of Ext-symmetry and the affine space structure of certain fibers, we introduce the notion of weighted quantum cluster functions and prove their multiplication formulas associated to abelian categories with…
In this paper, we study the abelian complexity $\rho_n^{ab}(\mathbf{t}^{(k)})$ of generalized Thue-Morse sequences $\mathbf{t}^{(k)}$. We obtain the exact value of $\rho_n^{ab}(\mathbf{t}^{(k)})$ for every integer $n\geq k$. Consequently,…
Due to the noncommutative nature of quaternions and octonions we introduce barred operators. This objects give the opportunity to manipulate appropriately the hypercomplex fields. The standard problems arising in the definitions of…
We have reviewed some results on quantized shuffling, and in particular, the grading and structure of this algebra. In parallel, we have summarized certain details about classical shuffle algebras, including Lyndon words (primes) and the…
We combine the language of monoids with the language of preorders so as to refine some fundamental aspects of the classical theory of factorization and prove an abstract factorization theorem with a variety of applications. In particular,…
We show that loop gravity can equally well be formulated in in terms of spinorial variables (instead of the group variables which are commonly used), which have recently been shown to provide a direct link between spin network states and…