Related papers: Combinatorics of Boson Normal Ordering: the Dobins…
We introduce new refinements of the Bell, factorial, and unsigned Stirling numbers of the first and second kind that unite the derangement, involution, associated factorial, associated Bell, incomplete Stirling, restricted factorial,…
The notion of the Fibonacci cobweb poset from [1] has been naturally extended to any admissible sequence $F$ in [2] where it was also recognized that the celebrated prefab notion of Bender and Goldman [3] - (see also [4,5]) - admits such an…
In this paper, we derive formal general formulas for noncommutative exponentiation and the exponential function, while also revisiting an unrecognized, and yet powerful theorem. These tools are subsequently applied to derive counterparts…
Originally motivated by questions of P. Etingof related to growth rates of tensor powers in symmetric tensor categories, we obtain general bounds on the order of finite subgroups of ${\rm GL}(n,\mathbb{C})$ with restricted composition…
We describe the most general local, Lorentz-invariant, effective field theory of scalars, fermions and gauge bosons up to mass dimension 6. We first obtain both a Green and a physical basis for such an effective theory, together with the…
We discuss algebraic and combinatorial aspects of the Hamiltonian normal form theory. The main objective is to describe the normal form near a singular point purely in terms of the original Hamiltonian, avoiding the normalization procedure.…
We derive a normal ordering formula for the operator \((xI)^n\), where \(I\) denotes the Volterra operator. The resulting coefficients are shown to coincide with the Bessel numbers. We also present two applications, along with a…
Normally ordered forms of functions of boson operators are important in many contexts in particular concerning Quantum Field Theory and Quantum Optics. Beginning with the seminal work of Katriel [Lett. Nuovo Cimento, 10(13):565--567, 1974],…
We show how series expansions of functions of bosonic number operators are naturally derived from finite-difference calculus. The scheme employs Newton series rather than Taylor series known from differential calculus, and also works in…
Composite particles made of two fermions can be treated as ideal elementary bosons as long as the constituent fermions are sufficiently entangled. In that case, the Pauli principle acting on the parts does not jeopardise the bosonic…
We derive new formulas for the number of unordered (distinct) factorizations with $k$ parts of a positive integer $n$ as sums over the partitions of $k$ and an auxiliary function, the number of partitions of the prime exponents of $n$,…
We investigate compositions of a positive integer with a fixed number of parts, when there are several types of each natural number. These compositions produce new relationships among binomial coefficients, Catalan numbers, and numbers of…
We derive a boson Hamiltonian from a Nuclear Hamiltonian whose potential is expanded in pairing multipoles and determine the fermion-boson mapping of operators. We use a new method of bosonization based on the evaluation of the partition…
We suggest some possible approaches of the unified equations of boson and fermion, which correspond to the unified statistics at high energy. A. The spin terms of equations can be neglected. B. The mass terms of equations can be neglected.…
Given an ordered set partition, when one insert a number of bars in-between the blocks of the ordered set partition the result is a barred preferential arrangement. In this study, using the notion of barred preferential arrangements we…
We define new norms for symmetric tensors over ordered normed spaces; these norms are defined by considering linear combinations of tensor products or powers of positive elements only. Relations between the different norms are studied. The…
We show that the compositions of positive integers may be interpreted in terms of powers of some power series, over arbitrary commutative ring. As consequences, several closed formulas for the compositions as well as for the generalized…
We present a close relationship between matching number, covering numbers and their fractional versions in combinatorial optimization and ordinary powers, integral closures of powers, and symbolic powers of monomial ideals. This…
Balancing numbers possess, as Fibonacci numbers, a Binet formula. Using this, partial sums of arbitrary powers of balancing numbers can be summed explicitly. For this, as a first step, a power $B_n^l$ is expressed as a linear combination of…
In [1] a new bosonization procedure has been illustrated, which allows to express a fermionic gaussian system in terms of commuting variables at the price of introducing an extra dimension. The Fermi-Bose duality principle established in…