Related papers: A combinatorial view of Holant problems on higher …
For any $n\geq 3$ and $ q\geq 3$, we prove that the {\sc Equality} function $(=_n)$ on $n$ variables over a domain of size $q$ cannot be realized by matchgates under holographic transformations. This is a consequence of our theorem on the…
Phase space of General Relativity is extended to a Poisson manifold by inclusion of the determinant of the metric and conjugate momentum as additional independent variables. As a result, the action and the constraints take a polynomial…
A generic PT-symmetric Hamiltonian is assumed tridiagonalized and truncated to N dimensions, and its up-down symmetrized special cases with J=[N/2] real couplings are considered. In the strongly non-Hermitian regime the secular equation…
In the paper, the family of conformal four-point ladder diagrams in arbitrary space-time dimensions is considered. We use the representation obtained via explicit calculation using the operator approach and conformal quantum mechanics to…
A quantum machine consisting of interacting linear clusters of atoms is proposed for the 3SAT problem. Each cluster with two relevant states of collective motion can be used to register a Boolean variable. Given any 3SAT Boolean formula the…
A novel polynomial expansion method of symmetric Boolean functions is described. The method is efficient for symmetric Boolean function with small set of valued numbers and has the linear complexity for elementary symmetric Boolean…
A function on a (generally infinite) graph $\G$ with values in a field $K$ of characteristic 2 will be called {\it harmonic} if its value at every vertex of $\G$ is the sum of its values over all adjacent vertices. We consider binary…
We study compositions whose parts are colored by subsequences of the Fibonacci numbers. We give explicit bijections between Fibonacci colored compositions and several combinatorial objects, including certain restricted ternary and…
We introduce two frameworks in order to deal with fractal and multi-fractal analysis for subset sum problems where some embedding into the $1$-dimensional Euclidean space plays an important role. As one of these frameworks, the notion of…
The Fibonacci number is the residue of a rational function, from which follows that Fibonacci number summation identities can be derived with the integral representation method, a method also used to derive combinatorial identities. A…
Boolean combinations allow combining given combinatorial objects to obtain new, potentially more complicated, objects. In this paper, we initiate a systematic study of this idea applied to graphs. In order to understand expressive power and…
Holographic algorithms, alternatively known as Pfaffian circuits, have received a great deal of attention for giving polynomial-time algorithms of $\#\mathsf{P}$-hard problems. Much work has been done to determine the extent of what this…
The Hankel determinant representations for the partition function and boundary correlation functions of the six-vertex model with domain wall boundary conditions are investigated by the methods of orthogonal polynomial theory. For specific…
With this work we aim to show how Mathematica can be a useful tool to investigate properties of combinatorial structures. Specifically, we will face enumeration problems on independent subsets of powers of paths and cycles, trying to…
The octagon abstract domain is a widely used numeric abstract domain expressing relational information between variables whilst being both computationally efficient and simple to implement. Each element of the domain is a system of…
Strongly simulating a quantum circuit, that is, computing an output amplitude, amounts to summing the circuit's Feynman paths, a weighted count over assignments to the Boolean ``path'' variables. The circuit's gates induce correlations…
We propose and develop a novel framework for analyzing permutation-based combinatorial optimization problems, which could eventually be extended to other types of problems. Our approach is based on the decomposition of the objective…
This study is devoted to the polynomial representation of the matrix $p$th root functions. The Fibonacci-H\"orner decomposition of the matrix powers and some techniques arisen from properties of generalized Fibonacci sequences, notably the…
We introduce a family of 3-variable "Farey polynomials" that are closely connected with the geometry and topology of $3$-manifolds and orbifolds as they can be used to produce concrete realisations of the boundaries and local coordinates…
Polynomial systems over the binary field have important applications, especially in symmetric and asymmetric cryptanalysis, multivariate-based post-quantum cryptography, coding theory, and computer algebra. In this work, we study the…