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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formula from 2s complement to decimal please

Hi what is the formula for an $n$ bit twos complement to decimal.. for example from $ n$ bit unsigned to decimal the formula is.. $\sum_{i=0}^{n-1} a_i 2^i$ from signed magnitude to decimal is ...
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Intersection of blocks of the symmetric BIBD $PG(d,q)$

The definition of a Balance Incomplete block design $(v,k,\lambda)$-BIBD can be found here. It is a well known fact (also see the link above) that every two blocks of a symmetric $(v,k,\lambda)$-BIBD ...
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Combinatorial Designs 1-Factorizations

Construct a starter of order 5 (on Z12) and from it construct a 1-factorization for K14.
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Upper bound for constant weight code L(n,d,w), with n=128, d=4

I would like to find an upper bound: L(n,d,w) <= f(n,d,w) for a constant weight code L(n,d,w), where w is the maximum weight, d is the Hamming distance between codes, and n is the code length. I ...
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Out of all combinations (n,k), largest set such that each combination overlaps with others by d or less.

This problem is relevant to determining the number of discriminable combinations of components in a sensory perception task. Suppose that there are N components to choose from, and we are only ...
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Design theory question

The question is: Prove that no (6, 3, 2)-BIBD can contain repeated blocks? I could not find a condition that determines whether a design has repeated blocks or not.
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How one can combine two covering designs?

There is a discussion on a science forum that how can one find small covering designs for lotto system. Namely, in that lotto we take seven numbers from the set $\{1,\ldots,39\}$ and we win if we have ...
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Small groups for church [closed]

I have a group of 20 families. Every quarter 5 families will meet together. The following three quarters ,famlies will be rotated so no families will be with the same families again. How do I set up ...
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Collection of subsets of $S$ where any $t$ have union equal to $S$ but any $t-1$ do not.

This recent question had me thinking about a generalization. Suppose we have a set of $n$ elements $S$. Suppose that we can assign the elements of $S$ to $b$ subsets $\{B_1,\ \cdots,\ B_b\}$ of $k$ ...
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1answer
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Hypergraph terminology

Suppose I have a hypergraph with vertices V and hyperedges H, where each hyperedge is a subset of V. I want to form a normal graph with vertex set V, where two vertices are adjacent if they lie in ...
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Decomposing $K_v - K_u$ into Hamilton paths where $v = u^2 - u + 1$.

A decomposition of a graph $G$ into subgraphs $H$ is a collection of graphs all isomorphic to $H$ which are edge-disjoint in $G$ and together cover all the edges of $G$. Let $u \geq 1$ and $v = u^2 ...
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Applications of Steiner Systems

I am looking for mathematical applications of Steiner systems (and other mathematical designs). The wikipedia article says that: This area is one of the oldest parts of combinatorics, such as in ...
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3answers
185 views

Symmetries of combinatorial structures.

Studying the automorphism groups of graphs/finite geometries/designs has been quite useful and important for both group theory and combinatorics. I know of the following books which cover the ideas ...
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16 views

Lower bound of maximum seating plans [duplicate]

10 people will sit in a row of 10 chairs. How do I calculate how many seating plans can be made, where two seating plan are considered the same if two plans share adjacent quadruples? or How can I ...
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2answers
167 views

France Olympiad Team Selection Test 2005

In an international meeting of n ≥ 3 participants, 14 languages are spoken. We know that: - Any 3 participants speak a common language. - No language is spoken by more than half of the participants. ...
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1answer
83 views

the table at the end of Theoretical Computer Science Cheat Sheet

Theoretical Computer Science Cheat Sheet, created by Steve Seiden, is a hodgepodge of well-known mathematical theorems and notions. I can understand (or guess at least) many of them, but I'm not sure ...
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3answers
295 views

How do you create projective plane out of a finite field?

I have heard and read unclear mentions of links between projective planes and finite fields. Is it possible to construct a projective plane (or a Steiner system) starting out with a field? Could you, ...
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2answers
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Choosing sets of vectors on a complex sphere

Consider a complex $t$ dimensional unit sphere. Can we have $t$ sets of $2^t$ vectors $v_{ij}\in \Bbb C^t$ on the sphere where $i=1$ to $t$ and $j=1$ to $2^t$ on this with inner products satisfying ...
5
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1answer
112 views

Number of combinations such that each pair of combinations has at most x elements in common?

I am doing research on the sense of smell and have a combinatorics problem: I have 128 different odors (n) and I mix them in mixtures of 10 (r). There are 2.26846154e+14 different mixtures. What I ...
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1answer
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How many different ways can the signs be chosen so that $\pm 1\pm 2\pm 3 … \pm (n-1) \pm n = n+1$?

How many different ways can the signs be chosen so that $\pm 1\pm 2\pm 3 ... \pm (n-1) \pm n = n+1$? This is an extension of this question: For what $n$ can $\pm 1\pm 2\pm 3 ... \pm (n-1) \pm n = ...
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1answer
272 views

What algorithm is a good to search a lotto design?

I'm interested what kind of algorithm would be suitable to find a lotto design? I saw that is has been proven that $L(39,7,4,7)=329$. This notation is explained in ...
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1answer
370 views

fabric design using trigonometric functions

is there any trigonometric function or any others that involve trigonometric function, that draw cool fabric shapes or patterns? I have seen some pictures like but with trigonometric functions... ...
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1answer
21 views

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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1answer
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combinatorial design problem

A combinatorial design has six varieties {1, 2, 3, 4, 5, 6}, and nine blocks of size 2. Every variety occurs in three blocks, and the design is simple. Prove that there are exactly two non-isomorphic ...
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Configuration analogues of projective spaces?

In a configuration, each point is incident to the same number of lines and each line is incident to the same number of points. The Fano plane is a configuration, with 3 points on each line, and 3 ...
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1answer
236 views

A generalization of Kirkman's schoolgirl problem

A friend of mine asked me this question. "I have $3n$ elements, and I want to know which is the maximum number of triplets $(a,b,c)$ so that no two triplets have more than one element in common". The ...
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2answers
127 views

Applications of design theory

I have recently started reading up on design theory, with the ultimate purpose of doing some original research in that area. I understand the mathematics fairly well, but am not understanding the ...
3
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2answers
117 views

Geometric solution to classic committee problem

Most people know the classic committe style problems. I read this solution to one of the basic version of the committe problem and was impressed, but not sure why it works. I was hoping someone ...
2
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1answer
68 views

Pairwise balanced designs

Let $X$ be a finite set containing $v$ elements and $\lambda$ be a positive integer. Let $K$ be a set of positive integers. Further let there be a multiset $\mathcal{B}$ containing subsets of $X$ ...
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1answer
62 views

Show that the complement of a difference set is a difference set

In combinatorics, a $(v,k,\lambda)$ difference set is a subset $D$ of cardinality $k$ of a group $G$ of order $v$ such that every nonidentity element of $G$ can be expressed as a product $d_1d_2^{-1}$ ...
4
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3answers
140 views

Orthogonal Latin Square 6*6

I need to make remarks about Tarry's Proof for the nonexistence of 6x6 Latin Squares as part of my final exam for a class I'm in. Problem is, I can't find it ANYWHERE on the internet. I can only find ...
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1answer
175 views

perfect binary e-error correcting code

let C be a perfect binary e-error correcting code of length n. assume 0 is a symbol and that 0 vector is a codeword.show that P={1,2,...,n} together with supports of codewords of weight 2e+1form an ...
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1answer
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Golf Round for a group of $12$

$12$ gentlemen wish to play $7$ rounds of golf. They want to split into $3$ groups of $4$ and play a different group each time with as much variety as possible without playing the same individuals ...
4
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1answer
202 views

Finding a system of sets resembling the projective plane

For every natural number $r$ I wish to construct a family of sets $\mathcal{F}$ such that Every set in $\mathcal{F}$ has cardinality $r$ and is a subset of $\{1,2,\ldots,r^2-r+1\},$ For every ...
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0answers
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Question related to designs where t= 2

1)Let D be a 2−(v,k,λ) design with b blocks and r blocks through every point. Let B be any block. How to show that the number of blocks that meet B is at least $k(r−1)^2/[(k−1)(λ−1)+(r−1)]$ 2) How to ...
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3answers
256 views

Question about members in sets

Let $A_1,A_2,...,A_n$ be sets with $k$ members in $A_i$ for every $1\le i\le n$. Suppose that the $A_i$ satisfy: 1) $|A_i\cap A_j| = 1$ for all $i\ne j$, 2) $A_1\cap A_2\cdots\cap A_n =\emptyset$. ...
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2answers
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combinatorics question from the real world

This is a real world scenario - please help. My brain hurts and I can't figure it out on my own. Suppose I host an event with the following constraints There will be exactly 5 lectures There will ...
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Name for a type of combinatorial design?

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 ...