06-1350/Class Notes for Thursday November 16

06-1350/Navigation Panel   # Week of... Links 1 Sep 11 About, Tue, Thu 2 Sep 18 Tue, Kurlin(P), Thu 3 Sep 25 Tue, Photo, Thu 4 Oct 2 HW1, Tue, Thu 5 Oct 9 Tue(P), Thu(P) 6 Oct 16 HW2, Tue(P), Thu(P) 7 Oct 23 Tue(P), Thu 8 Oct 30 HW3, Tue, Thu 9 Nov 6 Tue ([math]\displaystyle{ \nu }[/math]), Thu 10 Nov 13 Tue, Thu 11 Nov 20 HW4(P), Thu 12 Nov 27 Thu 13 Dec 4 Syzygies in Asymptote, Final Jan 8 Grades Note. (P) means "contains a problem that Dror cares about". Add your name / see who's in! On to 07-1352

In Preparation

The information below is preliminary and cannot be trusted! (v)

Today's Agenda

• Sweeping clean a tree and [math]\displaystyle{ {\mathcal A}(\Gamma)\equiv{\mathcal A}(\uparrow_{b_1(\Gamma)}) }[/math].

• [math]\displaystyle{ {\mathcal A}(\uparrow_n) }[/math] is a VS-algebra (see more at VS, TS and TG Algebras).
• In the coordinates above, write the [math]\displaystyle{ TR\Phi B }[/math] relations in various algebraic notations.
  • R4: [math]\displaystyle{ (1230)^\star B\cdot(1213)^\star B\cdot(1023)^\star\Phi=(1123)^\star\Phi\cdot(1233)^\star B }[/math] or [math]\displaystyle{ (B_{1a}B_{2a}\Phi_{1a}; B_{1b}B_{2b}; B_{1c}B_{2a}\Phi_{1b}; B_{2c}\Phi_{1c}) = (\Phi_{2a}B_{3a}; \Phi_{2a}B_{3b}; \Phi_{2b}B_{3c}; \Phi_{2c}B_{3c}) }[/math].
  • R3: [math]\displaystyle{ (1230)^\star B\cdot(1213)^\star B\cdot(1023)^\star B = (1123)^\star B\cdot(1203)^\star B\cdot(1231)^\star B }[/math] or [math]\displaystyle{ (B_{1a}B_{2a}B_{3a}; B_{1b}B_{2b}; B_{1c}B_{2a}B_{3b}; B_{2c}B_{3c}) = (B_{4a}B_{5a}B_{6a}; B_{4a}B_{5b}B_{6b}; B_{4b}B_{6c}; B_{4c}B_{5c}B_{6a}) }[/math].
  • R2: [math]\displaystyle{ (123)^\star B^\pm\cdot(132)^\star B^\mp=1_3 }[/math] or [math]\displaystyle{ (B^\pm_{1a}B^\mp_{2a}; B^\pm_{2b}B^\mp_{3c}; B^\pm_{1c}B^\mp_{2b}) = (1;1;1) }[/math].
  • R1: [math]\displaystyle{ (B^\pm_a; B^\pm_bB^\pm_c)=(1;T^{\pm 2}) }[/math].
  • Symmetry of [math]\displaystyle{ \Phi }[/math] and of [math]\displaystyle{ B^{\pm} }[/math].
  • [math]\displaystyle{ u }[/math], [math]\displaystyle{ d }[/math] and [math]\displaystyle{ \# }[/math]
  • Idempotence for [math]\displaystyle{ T }[/math], [math]\displaystyle{ R }[/math], [math]\displaystyle{ \Phi }[/math] and [math]\displaystyle{ B^{\pm} }[/math].
  • [math]\displaystyle{ B^{\pm} }[/math] in terms of [math]\displaystyle{ \Phi }[/math] and [math]\displaystyle{ R }[/math] and [math]\displaystyle{ R }[/math] in terms of [math]\displaystyle{ T }[/math].

General Principle. Believe not, until you see a running program.