A generalization of Connor's inequality to t-designs with automorphisms

AbstractIn this paper the incidence algebra for t-designs with automorphisms and the fundamental theorem discovered in [4] are exploited to obtain a generalization of Connor's inequality

Block-avoiding sequencings of points in Steiner triple systems

Given an STS(v), we ask if there is a permutation of the points of the design such that no l consecutive points in this permutation contain a block of the design. Such a permutation is called an l-good sequenc-ing. We prove that 3-good sequencings exist for any STS(v) with v\u3e3 and 4-good sequencings exist for any STS(v) with v\u3e71. Similar re-sults also hold for partial STS(v). Finally, we determine the existence or nonexistence of 4-good sequencings for all the nonisomorphic STS(v) with v =7, 9, 13 and 15

Block-avoiding sequencings of points in Steiner triple systems

Given an STS(v), we ask if there is a permutation of the points of the design such that no L consecutive points in this permutation contain a block of the design. Such a permutation is called an L-good sequencing. We prove that 3-good sequencings exist for any STS(v) with v\u3e3and 4-good sequencings exist for any STS(v) with v\u3e71. Similar results also hold for partial STS(v). Finally, we determine the existence or nonexistence of 4-good sequencings for all the nonisomorphic STS(v) with v=7,9,13 and 15

On min-base palindromic representations of powers of 2

A positive integer $N$ is \emph{palindromic in the base $b$} when $N = \sum_{i=0}^{k} c_i b^i$, $c_k\neq 0$,and $c_i=c_{k-i},\; i=0,1,2,...,k$, Focusing on powers of 2, we investigate the smallest base $b$ when $N=2^n$ is palindromic in the base $b$.Comment: 11 page

The 3-GDDs of type g3u2g^3u^2

A 3-GDD of type ${g^3u^2}$ exists if and only if $g$ and $u$ have the same parity, $3$ divides $u$ and $u\leq 3g$.Such a 3-GDD of type ${g^3u^2}$ is equivalent to an edge decomposition of $K_{g,g,g,u,u}$ into triangles

Super-simple (v,5,2)-designs

AbstractIn this paper we study the spectrum of super-simple (v,5,2)-designs. We show that a super-simple (v,5,2)-design exists if and only if v≡1 or 5(mod10),   v≠5,15, except possibly when v∈{75,95,115,135,195,215,231,285,365,385,515}