Related papers: Witness sets
We give an algorithm for enumerating the regular nontrivial partial difference sets (PDS) in the group $G_n = C_{2^n}\times C_{2^n}$. We use our algorithm to obtain all of these PDS in $G_n$ for $2\leq n\leq 9$, and we obtain partial…
We take the pre-sieved set to be all natural numbers $N=\{1,2,3,\dots\}$ with a sieve system:single sieve,double sieve,.... With single sieve, i.e. , remove out the multiple of a prime, we derive all the primes. With double sieve, i.e. ,…
In a recent paper, Amini et al. introduce a general framework to prove duality theorems between special decompositions and their dual combinatorial object. They thus unify all known ad-hoc proofs in one single theorem. While this…
We study weight modules of the Lie algebra $W_2$ of vector fields on ${\mathbb C}^2$. A classification of all simple weight modules of $W_2$ with a uniformly bounded set of weight multiplicities is provided. To achieve this classification…
During the past 20 years, the idea that non-spherical planetary nebulae (PN) may need a binary or planetary interaction to be shaped was discussed by various authors. It is now generally agreed that the varied morphologies of PN cannot be…
We consider a variant of the ABC Conjecture, attempting to count the number of solutions to $A+B+C=0$, in relatively prime integers $A,B,C$ each of absolute value less than $N$ with $r(A)<|A|^a, r(B)<|B|^b, r(C)<|C|^c.$ The ABC Conjecture…
A combinatorial characterization of measurable filters on a countable set is found. We apply it to the problem of measurability of the intersection of nonmeasurable filters.
A bijective proof is given for the following theorem: the number of compositions of n into odd parts equals the number of compositions of n + 1 into parts greater than one. Some commentary about the history of partitions and compositions is…
We give necessary conditions satisfied by the set of odd prime divisors of binary perfect polynomials. This allows us to get a new characterization of all the known perfect binary polynomials.
Quantum coherence is the key resource in quantum technologies including faster computing, secure communication and advanced sensing. Its quantification and detection are, therefore, paramount within the context of quantum information…
In this paper we present the set of saturated numerical semigroups with prime multiplicity. We also characterize the catenary degree of these semigroups that we acquire. The catenary degree of a numerical semigroup is the variant which…
We search a simplest and minimal way to determine whether a given quantum system is entangled or separable. For this end, we propose binary correlation measurements in which restricted knowledge of only zero or non-zero correlations is…
Being able to measure each merger's sky location, distance, component masses, and conceivably spins, ground-based gravitational-wave detectors will provide a extensive and detailed sample of coalescing compact binaries (CCBs) in the local…
Cepheids provide approaches to determining binary parameters which are often complementary to those for main sequence massive and intermediate mass stars. Specifically, we are using high resolution imaging, radial velocities, and X-ray…
This thesis generalizes the study of $C\cap(C + \alpha)$ where $C$ is the middle third Cantor set to self-affine sets in $\mathbb{R}^{n}$. We present sufficient and necessary conditions for when the translation $\alpha$ produces a…
The fundamental properties of detached eclipsing binary stars can be measured very accurately, which could make them important objects for constraining the treatment of convection in theoretical stellar models. However, only four or five…
We use a combinatorial approach to compute the number of non-isomorphic choices on four elements that can be explained by models of bounded rationality.
In this paper, a class of combinatorial identities is proved. A method is used which is based on the following rule: counting elements of a given set in two ways and making equal the obtained results. This rule is known as "counting in two…
We investigate rules which allow variable elimination in binary CSP (constraint satisfaction problem) instances while conserving satisfiability. We study variable-elimination rules based on the language of forbidden patterns enriched with…
Despite the recent progress of automated program verification techniques, fully automated verification of programs manipulating recursive data structures remains a challenge. We introduce solvable tuple patterns (STPs) and conjunctive STPs…