Related papers: New Steiner systems $S(2,6,v)$ with block length 6

This paper gives a construction of group divisible designs on the binary extension fields with block sizes 3, 4, 5, 6, and 7, respectively, which is motivated from the decoding of binary quadratic residue codes. A conjecture is proposed for…

It was proved in 2009 that any partial Steiner triple system of order $u$ has an embedding of order $v$ for each admissible integer $v\geq 2u+1$. This result is best-possible in the sense that, for each $u\geq 9$, there exists a partial…

We find a new highly symmetrical and very numerous class (millions of non-isomorphic sets) of 4-dim Kochen-Specker (KS) vector sets. Due to the nature of their geometrical symmetries, they cannot be obtained from previously known ones. We…

We prove new existence and nonexistence results for modular Golomb rulers in this paper. We completely determine which modular Golomb rulers of order $k$ exist, for all $k\leq 11$, and we present a general existence result that holds for…

In 2000, Rees and Shalaby constructed simple indecomposable two-fold cyclic triple systems for all v congruent to 0, 1, 3, 4, 7, and 9 (mod 12) where v = 4 or v>11, using Skolem-type sequences. We construct, using Skolem-type sequences,…

In this paper we construct, using Stark elements of Rubin [Ann. Inst. Fourier (Grenoble) 46 (1996), no. 1, 33-62], Kolyvagin systems for certain modified Selmer structures (that are adjusted to have core rank one in the sense of [Mem. Amer.…

We solve the long-standing open problem of classifying all 3-(v,k,1) designs with a flag-transitive group of automorphisms (cf. A. Delandtsheer, Geom. Dedicata 41 (1992), p. 147; and in: "Handbook of Incidence Geometry", ed. by F.…

A class of asteroids, called large super-fast rotators (large SFRs), have rotation periods shorter than 2 hours and diameters larger than ~ 0.3 km. They pose challenges to the usual interior rubble-pile structure unless a relatively high…

In this paper we present a graph theoretic construction of Steiner quadruple systems (SQS) admitting abelian groups as point-regular automorphism groups. The resulting SQS has an extra property which we call A-reversibility, where A is the…

A maximal arc of degree k in a finite projective plane P of order q = ks is a set of (q-s+1)k points that meets every line of P in either k or 0 points. The collection of the nonempty intersections of a maximal arc with the lines of P is a…

This paper is about the tiling dynamical systems approach to the study of aperiodic order. We compare and contrast four related types of systems: ordinary (one-dimensional) symbolic systems, one-dimensional tiling systems, multidimensional…

Modeling of materials systems for long times commonly requires the use of separation of time scale methods. We discuss this general approach and present two example systems, a-Si3B3N7 and the generation of homogeneous sinters.

This article continues our recent publication [I.A. Baburin and D.M. Proserpio and V.A. Saleev and A.V. Shipilova, Phys. Chem. Chem. Phys.17, 1332 (2015)] where we have presented a comprehensive computational study of sp3 carbon allotropes…

The V-systems are special finite sets of covectors which appeared in the theory of the generalized Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. Several families of V-systems are known but their classification is an open problem. We…

Recently, a construction of group divisible designs (GDDs) derived from the decoding of quadratic residue (QR) codes was given. In this paper, we extend the idea to obtain a new family of GDDs, which is also involved with a well-known…

We note that a strongly minimal Steiner $k$-Steiner system $(M,R)$ from (Baldwin-Paolini 2020) can be `coordinatized' in the sense of (Gantner-Werner 1975) by a quasigroup if $k$ is a prime-power. But for the basic construction this…

In the present paper, we study relative difference sets (RDSs) and linked systems of them. It is shown that a closed linked system of RDSs is always graded by a group. Based on this result, we also define a product of RDS linked systems…

The Yang-Baxter equation for a $SU(2)\times U(1)$-symmetric $S=1/2$ spin-orbital chain was solved using the special computer algorithm developed by the author. The 8 new $R$-matrices separated on 5 groups are presented. Among the obtained…

In this brief review, we introduce a new spin ladder system called skewed spin ladders and discuss the exotic quantum phases of this system. The spin ladders studied are the 5/7, 3/4 and 3/5 systems corresponding to alternately fused 5 and…

Kirkman triple systems (KTSs) are among the most popular combinatorial designs and their existence has been settled a long time ago. Yet, in comparison with Steiner triple systems, little is known about their automorphism groups. In…