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Operad: Ramanujan

abbreviation
Ram
category
dgvec
type
symetrique
dimensions

1, 2 - t, 6 - 8*t + 3*t**2, 24 -58*t + 50*t**2 - 15*t**3

Serie: ((1-t)*x/(1+x) + t*ln(1+x)).reverse()

properties
binary, quadratic, Hopf, Koszul
Koszul dual operad
Ram!
generateurs
  • generator E of type s[2] of degree 0
  • generator L of type s[1,1] of degree 0
  • generator Ω of type s[1,1] of degree 1
relations
  • relation: (xLy)Lz+(yLz)Lx+(zLx)Ly
  • equality: xE(yEz) = zE(xEy)
  • relation: xΩ(yLz)+xL(yΩz)+yΩ(zLx)+yL(zΩx)+zΩ(xLy)+zL(xΩy)
  • equality: xΩ(yEz) = yE(xΩz) + zE(xΩy)
  • equality: xL(yEz) = (xLy)Ez+yE(xLz)

References