JournalsaihpdVol. 8 , No. 1pp. 89–118

Enumerative gadget phenomena for (4, 1)-adinkras

  • Isaac Friend

    Brown University, Providence, USA
  • Jordan Kostiuk

    Brown University, Providence, USA
  • Yan X Zhang

    San José State University, USA
Enumerative gadget phenomena for (4, 1)-adinkras cover
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Abstract

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= 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 nn and kk parameters.

Cite this article

Isaac Friend, Jordan Kostiuk, Yan X Zhang, Enumerative gadget phenomena for (4, 1)-adinkras. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 8 (2021), no. 1 pp. 89–118

DOI 10.4171/AIHPD/98