TY - JOUR

T1 - Every latin hypercube of order 5 has transversals

AU - Perezhogin, Alexey L.

AU - Potapov, Vladimir N.

AU - Vladimirov, Sergey Yu

N1 - The research has been carried out within the framework of a state assignment of the Ministry of Education and Science of the Russian Federation for the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (project no. FWNF-2022-0017).

PY - 2024/11

Y1 - 2024/11

N2 - We prove that for all (Formula presented.) every latin (Formula presented.) -dimensional cube of order 5 has transversals. We find all 123 paratopy classes of layer-latin cubes of order 5 with no transversals. For each (Formula presented.) and (Formula presented.) we construct a (Formula presented.) latin (Formula presented.) -dimensional cuboid of order (Formula presented.) with no transversals. Moreover, we find all paratopy classes of nonextendible and noncompletable latin cuboids of order 5.

AB - We prove that for all (Formula presented.) every latin (Formula presented.) -dimensional cube of order 5 has transversals. We find all 123 paratopy classes of layer-latin cubes of order 5 with no transversals. For each (Formula presented.) and (Formula presented.) we construct a (Formula presented.) latin (Formula presented.) -dimensional cuboid of order (Formula presented.) with no transversals. Moreover, we find all paratopy classes of nonextendible and noncompletable latin cuboids of order 5.

KW - latin hypercube

KW - latin square

KW - nonextendible latin cuboid

KW - permanent of multidimensional matrix

KW - transversal

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85200028211&origin=inward&txGid=489c7d41e07f3a47c1c3bfffdd7dfa14

UR - https://www.mendeley.com/catalogue/fc70c553-f15b-34e8-8f5e-214580bb0954/

U2 - 10.1002/jcd.21954

DO - 10.1002/jcd.21954

M3 - Article

SP - 679

EP - 699

JO - Journal of Combinatorial Designs

JF - Journal of Combinatorial Designs

SN - 1063-8539

ER -