On a generalization of the seating couples problem
Copyright policy )On a generalization of the seating couples problem
We prove a conjecture of Adamaszek generalizing the seating couples problem to the case of $2n$ seats. Concretely, we prove that given a positive integer $n$ and $d_1,\ldots,d_n\in(\mathbb{Z}/2n)^*$ we can partition $\mathbb{Z}/2n$ into $n$ pairs with differences $d_1,\ldots,d_n$.
3 pages
- National Scientific and Technical Research Council Argentina
- University of Buenos Aires Argentina
- Facultad de Ciencias Agrarias y Forestales Argentina
couples, Combinatorial aspects of partitions of integers, SEATING, PARTITION, 11B13, 05B10, Exact enumeration problems, generating functions, SUMSET, partition, CAUCHY–DAVENPORT, Primes, seating, Cauchy-Davenport theorem, Other combinatorial number theory, FOS: Mathematics, https://purl.org/becyt/ford/1.1, sumset, Mathematics - Combinatorics, Combinatorics (math.CO), https://purl.org/becyt/ford/1, COUPLES
couples, Combinatorial aspects of partitions of integers, SEATING, PARTITION, 11B13, 05B10, Exact enumeration problems, generating functions, SUMSET, partition, CAUCHY–DAVENPORT, Primes, seating, Cauchy-Davenport theorem, Other combinatorial number theory, FOS: Mathematics, https://purl.org/becyt/ford/1.1, sumset, Mathematics - Combinatorics, Combinatorics (math.CO), https://purl.org/becyt/ford/1, COUPLES
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