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Annales de l’Institut Henri Poincaré D

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Volume 8, Issue 1, 2021, pp. 89–118
DOI: 10.4171/AIHPD/98

Published online: 2021-03-01

Enumerative gadget phenomena for (4, 1)-adinkras

Isaac Friend[1], Jordan Kostiuk[2] and Yan X Zhang[3]

(1) Brown University, Providence, USA
(2) Brown University, Providence, USA
(3) San José State University, USA

Adinkras are combinatorial objects developed to study supersymmetry representations. Gates et al. introduced the gadget as a function of pairs of adinkras, obtaining some mysterious results for ($ = 4, k = 1$) adinkras with computer-aided computation. Specifically, very few values of the gadget actually appear, suggesting a great deal of symmetry in these objects. In this paper, we compute gadgets symbolically and explain some of these observed phenomena with group theory and combinatorics. Guided by this work, we give some suggestions for generalizations of the gadget to other values of the $n$ and $k$ parameters.

Keywords: Adinkras, supersymmetry, gadgets, inner products

Friend Isaac, Kostiuk Jordan, Zhang Yan: Enumerative gadget phenomena for (4, 1)-adinkras. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 8 (2021), 89-118. doi: 10.4171/AIHPD/98