TY - JOUR
T1 - Toward a Solution of Archdeacon's Conjecture on Integer Heffter Arrays
AU - Pellegrini, Marco Antonio
AU - Traetta, Tommaso
PY - 2025
Y1 - 2025
N2 - In this article, we make significant progress on a conjecture proposed by Dan Archdeacon on the existence of integer Heffter arrays H(m, n; s, k) whenever the necessary conditions hold, that is, 3 ⩽ s ⩽n, 3 ⩽ k ⩽m, ms = nk and nk ≡ 0, 3 (mod 4). By constructing integer Heffter array sets, we prove the conjecture in the affirmative whenever k ⩾ s gcd( s, k ) is odd and s ≠ 3, 5, 6, 10.
AB - In this article, we make significant progress on a conjecture proposed by Dan Archdeacon on the existence of integer Heffter arrays H(m, n; s, k) whenever the necessary conditions hold, that is, 3 ⩽ s ⩽n, 3 ⩽ k ⩽m, ms = nk and nk ≡ 0, 3 (mod 4). By constructing integer Heffter array sets, we prove the conjecture in the affirmative whenever k ⩾ s gcd( s, k ) is odd and s ≠ 3, 5, 6, 10.
KW - Heffter array
KW - Heffter array set
KW - combinatorial array
KW - Heffter array
KW - Heffter array set
KW - combinatorial array
UR - https://publicatt.unicatt.it/handle/10807/312216
UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=105005777753&origin=inward
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105005777753&origin=inward
U2 - 10.1002/jcd.21983
DO - 10.1002/jcd.21983
M3 - Article
SN - 1063-8539
SP - 310
EP - 323
JO - Journal of Combinatorial Designs
JF - Journal of Combinatorial Designs
IS - 33
ER -