TY - JOUR

T1 - Egalitarian Steiner quadruple systems of doubly even order

AU - Colbourn, Charles J.

N1 - Funding Information:
The work was supported by NSF grant CCF 1816913 .
Publisher Copyright:
© 2022 Elsevier B.V.

PY - 2022/7

Y1 - 2022/7

N2 - Ordering the blocks of a design, the point sum of an element is the sum of the indices of blocks containing that element. Block labelling for popularity asks for the point sums to be as equal as possible. When all point sums are equal, the system is egalitarian; when point sums differ by at most one, it is almost egalitarian. For Steiner quadruple systems, a doubling construction is adapted to establish that an egalitarian S(3,4,v) exists whenever v≡4,20(mod24) and that an almost egalitarian S(3,4,v) exists whenever v≡8,16(mod24) and v≠8.

AB - Ordering the blocks of a design, the point sum of an element is the sum of the indices of blocks containing that element. Block labelling for popularity asks for the point sums to be as equal as possible. When all point sums are equal, the system is egalitarian; when point sums differ by at most one, it is almost egalitarian. For Steiner quadruple systems, a doubling construction is adapted to establish that an egalitarian S(3,4,v) exists whenever v≡4,20(mod24) and that an almost egalitarian S(3,4,v) exists whenever v≡8,16(mod24) and v≠8.

KW - Difference sum labelling

KW - Egalitarian labelling

KW - Steiner quadruple system

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U2 - 10.1016/j.disc.2022.112887

DO - 10.1016/j.disc.2022.112887

M3 - Article

AN - SCOPUS:85126564435

SN - 0012-365X

VL - 345

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 7

M1 - 112887

ER -