Imbalance in tournament designs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F01%3A00000928" target="_blank" >RIV/61989100:27240/01:00000928 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Imbalance in tournament designs
Original language description
A tournament design (TD) is a quadruple $(V,F,P,alpha)$ where $V$ is a $2n$-element set whose elements are teams, $F={F_1,F_2,dots,F_{2n-1}}$ is a set of 1-factorizations such that $(V,F)$ is a 1-factorization of $K_{2n}$, and $alpha =(alpha_1,dots,alpha_{2n-1})$ is a field assignment, i.e. the $alpha_i $ maps the $n$ 2-subsets of $F_i$ onto the set of fields $P$. The appearance matrix of a tournament design TD$(n)$ is an $n times 2n$ matrix $A=(a_{ij})$ where the entry $a_{ij}$ is the numberof times the team $T_j$ plays on the field $P_i$. This paper introduces two measures of imbalance, team imbalance and field imbalance. Both of these are defined in terms of the appearance matrix. The team imbalance of the team $T_j$, $I_T(j)$, is the maximum over $i$ and $k$ of ${|a_{ij} - a_{kj}|: i,k in {1,dots,n}}$, and the total team imbalance $text{IT}(D)$ of the tournament design $D$ is $sum_{j=1}^{2n} I_T(j)$. Similarly, the field imbalance of the field $P_i$, $I_F(i)$, is
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2001
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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