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  • Catalan number
  • For example, the following are the Dyck words up to length 6: XY XXYY     XYXY XXXYYY     XYXXYY     XYXYXY     XXYYXY     XXYXYY Re-interpreting the symbol

  • Knuth–Bendix completion algorithm
  • xyxyx^{3}} by overlapping (1) and (5), we get x y x y = y 2 x 2 {\displaystyle xyxy=y^{2}x^{2}} , so we add the rule These obsolete rules (4) and (5), so we

  • Square (algebra)
  • x y = x x y y = x 2 y 2 . {\displaystyle \forall x,y\in A\quad (xy)^{2}=xyxy=xxyy=x^{2}y^{2}.} In the language of quadratic forms, this equality says

  • Matsumoto's theorem (group theory)
  • transformed into the second by repeatedly transforming xyxy... to yxyx... (or vice versa) where xyxy... = yxyx... is one of the defining relations of the

  • Magnetic levitation
  • stand for X and Y direction movement. From top to bottom, the order comes in XYXY that cross each other evenly and same axis were interlaced to control actuation

  • Heisenberg group
  • rotations by 90°. The other reflections are xyx and yxy, and rotation by 180° is xyxy (= yxyx). The Lie algebra h {\displaystyle {\mathfrak {h}}} of the Heisenberg

  • Rotation formalisms in three dimensions
  • square: the bivector x̂ŷ describes the xy-plane. Its square is (x̂ŷ)2 = x̂ŷx̂ŷ. Because the unit basis vectors are orthogonal to each other, the geometric

  • Coxeter group
  • x y x y = 1 {\displaystyle xyxy=1} implies that x y = x ( x y x y ) y = ( x x ) y x ( y y ) = y x {\displaystyle xy=x(xyxy)y=(xx)yx(yy)=yx} . Alternatively

  • Opposite ring
  • x 2 y x + 3 y x y , {\displaystyle {\begin{aligned}(2x^{2}yx+3yxy)*(xyxy+1)&=(xyxy+1)\cdot (2x^{2}yx+3yxy)\\&=2xyxyx^{2}yx+3xyxy^{2}xy+2x^{2}yx+3yxy,\end{aligned}}}

  • Unavoidable pattern
  • x y x x , x x y x y , x y x y y {\displaystyle xx,xxy,xyy,xxyx,xxyy,xyxx,xyxy,xyyx,xxyxx,xxyxy,xyxyy} have avoidability index of 3. others have avoidability

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Astrological/horoscope meaning of xyxys. xyxys means: undefined

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    X: Meaning of X in the acronym xyxys means: X is a cross bettween two arms of exactly the same lenght. It also balances on two ends at the bottom. It looks like Y with the bottom ends merged in the middle. X is stable, responsible, gorgeous, and spiritual as it opens upwards. X also shows enlightenment as it seeks to explore by extending its arms.

    Y: Meaning of Y in the acronym xyxys means: Y is a mystic character. It lies on one leg spreading two arms out upwards and outwards. Y seems to be yearning for something from above. It is mystic, reserved, affecting yet self-governing. The separate arms shows why is separate and it could also be troublesome if it receives mystical powers.

    S: Meaning of S in the acronym xyxys means: S is a single strand that goes forward and backwards. It shows a willingness to explore. Friendliness, perceptiveness and accommodating are all S qualities. The ends pointing forward and backwards shows a conflicting nature with itself and a degree of puzzlement.

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