Related papers: Switching for 2-designs
Due to their important applications to coding theory, cryptography, communications and statistics, combinatorial $t$-designs have been attracted lots of research interest for decades. The interplay between coding theory and $t$-designs has…
An automorphism group of an incidence structure I induces a tactical decomposition on I. It is well known that tactical decompositions of t-designs satisfy certain necessary conditions which can be expressed as equations in terms of the…
2-in-1 design (Chen et al. 2018) is becoming popular in oncology drug development, with the flexibility of using different endpoints at different decision time. Based on the observed interim data, sponsors choose either to seamlessly…
A characterization of $\mathbb{Z} _t \times \mathbb{Z}_2^2$-cocyclic Hadamard matrices is described, depending on the notions of {\em distributions}, {\em ingredients} and {\em recipes}. In particular, these notions lead to the…
The paper deals with recursive constructions for simple 3-designs based on other 3-designs having $(1, \sigma)$-resolution. The concept of $(1, \sigma)$-resolution may be viewed as a generalization of the parallelism for designs. We show…
The chromatic index of a cubic graph is either 3 or 4. Edge-Kempe switching, which can be used to transform edge-colorings, is here considered for 3-edge-colorings of cubic graphs. Computational results for edge-Kempe switching of cubic…
We have extended the Paley constructions for Hadamard matrices and obtained some series of Hadamard matrices. Especially Paley construction-II is applicable for odd prime power q is congruent to 1(mod 4) however our method is applicable for…
The dual codes of the ternary linear codes of the residual designs of biplanes on 56 points are used to prove the nonexistence of quasi-symmetric 2-$(56,12,9)$ and 2-$(57,12,11)$ designs with intersection numbers 0 and 3, and the…
In this note, we present two new identities for derangements. As a corollary, we have a combinatorial proof of the irreducibility of the standard representation of symmetric groups.
Switched systems constitute an important modeling paradigm faithfully describing many engineering systems in which software interacts with the physical world. Despite considerable progress on stability and stabilization of switched systems,…
We give a new perspective of the relationship between simple matroids of rank 3 and pairwise balanced designs, connecting Wilson's theorems and tools with the theory of truncated boolean representable simplicial complexes. We also introduce…
The circulant real and complex matrices are used to find new real and complex conference matrices. With them we construct Sylvester inverse orthogonal matrices by doubling the size of inverse complex conference matrices. When the free…
Some skew-symmetrizable integer exchange matrices are associated to ideal (tagged) triangulations of marked bordered surfaces. These exchange matrices admits unfoldings to skew-symmetric matrices. We develop an combinatorial algorithm that…
In this paper, we study skew-symmetric $2$-$\{v;r,k;\lambda\}$ supplementary difference sets related to a certain class of complex spherical 2-codes. A classification of such supplementary difference sets is complete for $v \le 51$.
In this paper, we define a new identity for twice differentiable mappings and obtained some new estimates on the generalization of Hadamard's and Simson's type inequalities for quasi-geometrically convex mappings using of this identity.
A closed formula multiallelic Walsh (or Hadamard) transform is introduced. Basic results are derived, and a statistical interpretation of some of the resulting linear forms is discussed.
A classical method of constructing a linear code over $\gf(q)$ with a $t$-design is to use the incidence matrix of the $t$-design as a generator matrix over $\gf(q)$ of the code. This approach has been extensively investigated in the…
In this article, we give a polynomial algorithm to decide whether a given permutation $\sigma$ is sortable with two stacks in series. This is indeed a longstanding open problem which was first introduced by Knuth. He introduced the stack…
We present a new construction of triple arrays by combining a symmetric 2-design with a resolution of another 2-design. This is the first general method capable of producing non-extremal triple arrays. We call the triple arrays which can be…
A design is $G$-additive with $G$ an abelian group, if its points are in $G$ and each block is zero-sum in $G$. All the few known ``manageable" additive Steiner 2-designs are $\mathrm{EA}(q)$-additive for a suitable $q$, where…