https://m2.mtmt.hu/ hun 2026-04-30 05:40 JournalArticle 3395278 APPROVED true Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 13 Reáltanoda street, Budapest, 1053, Hungary Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, United Kingdom Institute of Mathematics, Eötvös University, 1/C Pázmány P. sétány, Budapest, 1117, Hungary Export Date: 3 January 2019 Correspondence Address: Tóth, G.; Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 13 Reáltanoda street, Hungary; email: toth@renyi.hu Funding details: 267165 Funding details: TÉT 12 MX-1-2013-0006 Funding details: K 111827 Funding details: 648017 Funding details: 750857 Funding details: K 116769 Funding details: 306493 Funding text 1: ∗Corresponding author. †IB was supported by ERC Advanced Research Grant no 267165 (DISCONV) and by National Research, Development and Innovation Office NKFIH Grants K 111827 and K 116769. ‡ECs was supported by ERC grants 306493 and 648017 and by Marie Curie Fellowship, grant No. 750857. §GyK was partially supported by bilateral research grant TÉT 12 MX-1-2013-0006. ¶GT was supported by the National Research, Develpoment and Innovation Office NKFIH Grant K 111827. Key words and phrases: sequence, block partition, transversal. Mathematics Subject Classification: primary 05A18, secondary 52C99. Funding Agency and Grant Number: ERC Advanced Research Grant [267165]; National Research, Development and Innovation Office NKFIH [K 111827, K 116769]; ERC [306493, 648017]; Marie Curie Fellowship [750857]; National Research, Develpoment and Innovation Office NKFIH Grant [K 111827]; [TET 12 MX-1-2013-0006] Funding text: IB was supported by ERC Advanced Research Grant no 267165 (DISCONV) and by National Research, Development and Innovation Office NKFIH Grants K 111827 and K 116769.; ECs was supported by ERC grants 306493 and 648017 and by Marie Curie Fellowship, grant No. 750857.; GyK was partially supported by bilateral research grant TET 12 MX-1-2013-0006.; GT was supported by the National Research, Develpoment and Innovation Office NKFIH Grant K 111827. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 13 Reáltanoda street, Budapest, 1053, Hungary Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, United Kingdom Institute of Mathematics, Eötvös University, 1/C Pázmány P. sétány, Budapest, 1117, Hungary Export Date: 16 September 2019 Correspondence Address: Tóth, G.; Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 13 Reáltanoda street, Hungary; email: toth@renyi.hu Funding details: 267165 Funding details: TÉT 12 MX-1-2013-0006, K 111827, 648017, 750857, K 116769, 306493 Funding text 1: ∗Corresponding author. †IB was supported by ERC Advanced Research Grant no 267165 (DISCONV) and by National Research, Development and Innovation Office NKFIH Grants K 111827 and K 116769. ‡ECs was supported by ERC grants 306493 and 648017 and by Marie Curie Fellowship, grant No. 750857. §GyK was partially supported by bilateral research grant TÉT 12 MX-1-2013-0006. ¶GT was supported by the National Research, Develpoment and Innovation Office NKFIH Grant K 111827. Key words and phrases: sequence, block partition, transversal. 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The size b of a block B is the sum of its elements. It is proved in [1] that for each positive integer n, there is a partition of S into n blocks B (1), B (n) with for every i, j. 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Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, United Kingdom Institute of Mathematics, Eötvös University, 1/C Pázmány P. sétány, Budapest, 1117, Hungary Export Date: 3 J...</pre> </div></div>