# Tagged Questions

For questions about Combinatorial design theory, a part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry. The theory has applications in the area of the design ...

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### Terminology - variant of a hypergraph

In a hypergraph, we have vertices $V$ and hyperedges $H$, where each hyperedge is a subset of $V$. Suppose that we would like the hyperedges to be (ordered) tuples, rather than subsets. Does this ...
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### Orthogonal arrays - relation to software testing, is that sample true?

When doing ortohognal arrays testing, the process is like this: Consider a function with 3 variables,each with 3 options. 3 pairs, each with 3*3 values = 27 parametric pairs. Each "function call" ...
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### Trying to find a combinatorial design which describes my problem

A group of 8 golfers would like to play in teams, split into two teams of 4, with a different arrangement of teams on each of 5 consecutive days; they would like each pair of players to be on the same ...
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### Find a (16,6,1) Balanced incomplete block design (BIBD)

I'm trying to find a balanced incomplete block design with the 16 items and $\lambda= 1$. I've calculated (using these defenitions) that a BIBD with 8 blocks and 6 items per block should be possible. ...
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### balanced incomplete designs

My textbook said a balanced design with covalency 0 is a complete design. I don't understand this, because \begin{gather} \text{set of varieties}=\{v_1,v_2,v_3\}\\ B_1 = \{v_1\},\\ B_2 = ...
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### Number of blocks in this design $(V,\mathcal{B})$ $|V|=16$ and $\mathcal{B}$ has size $4$

Let $(V,\mathcal{B})$ be a design in which $|V|=16$, each block in $\mathcal{B}$ has size $4$, and each pair of points occurs in precisely one block. How many blocks are in this design? Try 1: ...
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### Symmetric Balanced Incomplete Block Design Example with (56,7,1)

Can someone give an example of Symmetric Balanced Incomplete Block design with (56,7,1). That is v=b=56,k=r=7, $\Lambda = 1$.
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### A proof regarding a symmetric $(v, k, \lambda)$-design.

I've been asked to prove the following; Consider a symmetric $(v,k,\lambda)$-design where $2k < v$. Prove that $2\lambda < k$. Now, being a symmetric design, I know that $v = b$, $r = k$, ...
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### network design: why can't an almost satisfied proper function violated by all given sets?

I'm reading a book about (survivable) network design and i have a problem understanding a lemma. Given an undirected graph G and $V(G)$ its nodes and $E(G)$ its edges. The book defines a proper ...
Consider the $2 - (4t-1, 2t, t)$ design where $t$ is an odd number and $A$ is the incidence matrix. I suspect that the number of elements with value $1$ in each row of $A$ is equal to $2t$ but I can't ...
Let $X$ be a ground set, and consider a collection $\mathscr{S}$ of subsets of $X$, $\mathscr{S} = \{S_1, \dots, S_n\}$. We would like to find a collection $\mathscr{S}'$ with the property that for ...