Related papers: A few more Hadamard Partitioned Difference Familie…
If $D$ is a $(4u^2,2u^2-u,u^2-u)$ Hadamard difference set (HDS) in $G$, then $\{G,G\setminus D\}$ is clearly a $(4u^2,[2u^2-u,2u^2+u],2u^2)$ partitioned difference family (PDF). Any $(v,K,\lambda)$-PDF will be said of Hadamard-type if…
Let $v$ be a positive odd integer. A $(v,k,\lambda)$-perfect difference family (PDF) is a collection $\mathcal{F}$ of $k$-subsets of $\{0,1,\ldots,v-1\}$ such that the multiset $\bigcup_{F\in \mathcal{F}}\{x-y : x,y\in F, x>y\}$ covers each…
Motivated by the application in geometric orthogonal codes (GOCs), Wang et al. introduced the concept of generalized perfect difference families (PDFs), and established the equivalence between GOCs and a certain type of generalized PDFs…
We introduce the concept of a disjoint partial difference family (DPDF) and an external partial difference family (EPDF), a natural generalisation of the much-studied structures of disjoint difference family (DDF), external difference…
Perfect difference families (PDFs for short) are important both in theoretical and in applications. Perfect difference matrices (PDMs for short) and the equivalent structure had been extensively studied and used to construct perfect…
We present a methodology for the construction of parton distribution functions (PDFs) designed to provide an accurate representation of PDF uncertainties for specific processes or classes of processes with a minimal number of PDF error…
A skew Hadamard difference set (SHDS) is a difference set that satisfies the skew condition. It is known that if a group G admits a skew hadamard difference set, then G is a p-group with order congruent to 3 modulo 4. We will generalize…
Using a class of permutation polynomials of $F_{3^{2h+1}}$ obtained from the Ree-Tits symplectic spreads in $PG(3,3^{2h+1})$, we construct a family of skew Hadamard difference sets in the additive group of $F_{3^{2h+1}}$. With the help of a…
Parton distribution functions (PDFs) are nonperturbative quantities describing the relation between a hadron and quarks and gluons within it. We propose to extract PDFs from QCD global analysis of "data" generated by lattice QCD…
A partial Hadamard matrix is a matrix $H\in M_{M\times N}(\mathbb T)$ whose rows are pairwise orthogonal. We associate to each such $H$ a certain quantum semigroup $G$ of quantum partial permutations of $\{1,...,M\}$ and study the…
Complex Hadamard matrices, consisting of unimodular entries with arbitrary phases, play an important role in the theory of quantum information. We review basic properties of complex Hadamard matrices and present a catalogue of inequivalent…
Recently, new combinatorial structures called disjoint partial difference families (DPDFs) and external partial difference families (EPDFs) were introduced, which simultaneously generalize partial difference sets, disjoint difference…
A disjoint $(v,k,k-1)$ difference family in an additive group $G$ is a partition of $G\setminus\{0\}$ into sets of size $k$ whose lists of differences cover, altogether, every non-zero element of $G$ exactly $k-1$ times. The main purpose of…
Assume $\lambda=\{k_1,k_2, \ldots, k_q\}$ is a partition of $k_{\lambda} = \sum_{i=1}^q k_i$. A $\lambda$-list assignment of $G$ is a $k_\lambda$-list assignment $L$ of $G$ such that the colour set $\bigcup_{v \in V(G)}L(v)$ can be…
Complex Hadamard matrices H of order 6 are characterized in a novel manner, according to the presence/absence of order 2 Hadamard submatrices. It is shown that if there exists one such submatrix, H is equivalent to a Hadamard matrix where…
It is anticipated that hard double parton scatterings will occur frequently in the collisions of the LHC, producing interesting signals and significant backgrounds to certain single scattering processes. For double scattering processes in…
In the framework of quantum chromodynamics (QCD), parton distribution functions (PDFs) quantify how the momentum and spin of a hadron are divided among its quark and gluon constituents. Two main approaches exist to determine PDFs. The first…
Let $\hat{\boldsymbol x}$ be a normalised standard complex Gaussian vector, and project an Hermitian matrix $A$ onto the hyperplane orthogonal to $\hat{\boldsymbol x}$. In a recent paper Faraut [Tunisian J. Math. \textbf{1} (2019),…
Partition functions, also known as homomorphism functions, form a rich family of graph invariants that contain combinatorial invariants such as the number of k-colourings or the number of independent sets of a graph and also the partition…
Skew Hadamard difference sets are an interesting topic of study for over seventy years. For a long time, it had been conjectured the classical Paley difference sets (the set of nonzero quadratic residues in $\mathbb{F}_q$ where $q \equiv 3…