相关论文: Roman and Vatican Crossover Designs
Scalable quantum computing is fundamentally bottlenecked not by qubit count or fabrication yield, but by a rigid temporal mismatch: macroscopic classical coordination latency ($\tau_c$) inevitably grows with system diameter, while…
By making use of the generalized concept of orthogonality in Latin squares, certain t-partite graphs have been constructed and a suggestion for a net work system and some applications have been made.
Quasi-complementary sequence sets (QCSSs) can be seen as a generalized version of complete complementary codes (CCCs), which enables multicarrier communication systems to support more users. The contribution of this work is two-fold. First,…
Scripting code may present maintenance problems in the long run. There is, then, the call for methodologies that make it possible to control the properties of programs written in dynamic languages in an automatic fashion. We introduce…
A quantum Latin square of order $v$, QLS($v$), is a $v\times v$ array in which each of entries is a unit column vector from the Hilbert space $\mathbb{C}^{v}$, such that every row and column forms an orthonormal basis of $\mathbb{C}^{v}$.…
A Catalan pair is a pair of binary relations (S,R) satisfying certain axioms. These objects are enumerated by the well-known Catalan numbers, and have been introduced with the aim of giving a common language to most of the structures…
In 1974 Allan Cruse provided necessary and sufficient conditions to extend an $r\times s$ partial latin rectangle consisting of $t$ distinct symbols to a latin square of order $n$. Here we provide some generalizations and consequences of…
Applications of graph colouring often involve taking restrictions into account, and it is desirable to have multiple (disjoint) solutions. In the optimal case, where there is a partition into disjoint colourings, we speak of a packing.…
A latin bitrade is a pair of partial latin squares which are disjoint, occupy the same set of non-empty cells, and whose corresponding rows and columns contain the same set of entries. Dr\'apal (\cite{Dr9}) showed that a latin bitrade is…
We analyze a supersymmetric system with four flat directions. We observe several interesting properties, such as the coexistence of the discrete and continuous spectrum in the same range of energies. We also solve numerically the classical…
Computer experiments with both qualitative and quantitative input variables occur frequently in many scientific and engineering applications. How to choose input settings for such experiments is an important issue for accurate statistical…
We explore partitions that lie in the intersection of several sets of classical interest: partitions with parts indivisible by $m$, appearing fewer than $m$ times, or differing by less than $m$. We find results on their behavior and…
This is a translation of Leonhard Euler's ``De quadratis magicis'' . It is E795 in the Enestrom index. This paper studies how to construct magic squares with certain numbers of cells, in particular 9, 16, 25 and 36. It considers some…
Roman-type domination parameters form an important class of graph invariants that model protection and resource allocation problems on networks. Among them, $[k]$-Roman domination provides a unified framework that generalizes Roman, double…
A Latin square of order $n$ with symbols $a_1,\ldots,a_n$ can be considered as a multiplication table for binary operation in the set $A=\{a_1,\ldots,a_n\}$. We prove that, if this operation is associative, then $A$ is a group.
Symmetries of combinatorial objects are known to complicate search algorithms, but such obstacles can often be removed by detecting symmetries early and discarding symmetric subproblems. Canonical labeling of combinatorial objects…
A latin bitrade (T1, T2) is a pair of partial latin squares which are disjoint, occupy the same set of non-empty cells, and whose corresponding rows and columns contain the same set of entries. A genus may be associated to a latin bitrade…
A crossover trial is an efficient trial design when there is no carry-over effect. To reduce the impact of the biological carry-over effect, a washout period is often designed. However, the carry-over effect remains an outstanding concern…
This is a companion note to the paper "Almost all Steiner triple systems have perfect matchings (arXiv:1611.02246). That paper contains several general lemmas about random Steiner triple systems; in this note we record analogues of these…
A Costas latin square of order n is a set of n disjoint Costas arrays of the same order. Costas latin squares are studied here from a construction as well as a classification point of view. A complete classification is carried out up to…