On the score sheets of a round-robin football tournament |
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| Affiliation: | 1. Simion Stoilow Institute of Mathematics of the Romanian Academy, Research Unit 5, P.O. Box 1-764, 014700 Bucharest, Romania;2. Universitat Jaume I, Campus de Riu Sec, Departamento de Matemáticas & Institut Universitari de Matemàtiques i Aplicacions de Castelló, 12071 Castellón de la Plana, Spain |
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| Abstract: | The set of (ordered) score sheets of a round-robin football tournament played between n teams together with the pointwise addition has the structure of an affine monoid. In this paper we study (using both theoretical and computational methods) the most important invariants of this monoid, namely the Hilbert basis, the multiplicity, the Hilbert series and the Hilbert function. |
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| Keywords: | Score sheets Affine monoids Hilbert basis Multiplicity Hilbert series |
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