Advanced paper aicraft construction by Morris PDF

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X12 ~ Xij. A n a l o g o u s l y , X22 ~ X 1 2 . On t h e o t h e r hand, X21. XI2 ~_ X22 and XI2. X21 ~_ XII imply XI2 ~ X22 and XI2 ~_ Xll. Thus XI2 ~ XII ~ X22. 5. 3. D. Proposition. ~j s u c h t h a t equivaIency relation. Proof. X=(Xij)i ,jeI In p a r t i c u l a r , Let i ~j, j ~k. = d ( e n ) = d ( e n , ) =1. mutation matrices, be a s t a t i o n a r y g r a p h . d ( e m ) = d ( e m ) = 1. I =q)I t the m a t r i x e Then this reiation (a d i s j o i n t u n i o n ) w h e r e Let us take emCXij, Then emenCXik, Let us write and since enCXjk ~ is a n i , j e i t iff with d(em) = d(em, ) = e m { x .

It h a s three basic graphs: e 0 : loops, graph; ~ el: e 2 : the c o m p l e m e n t a r y g r a p h of e 1. i. Z. 5. 2. Examples Lemma. Let of imprimitive cells are constructed in G3, 4. ~ b e a n o r m a l subcell of a cell ~ . If C = ~]i< kei (in the assumptions of I. i) has a block-triangular form, then it can be brought into block-diagonal form, such that diagonal blocks contain no zeros and have pairwise equal degrees. Proof. -i1 fk and f~. T h e y have the following form: T 1 1 fk = fk = \ 0 \ <----v d 1 1 ~..

K ai~~s k ~ a _. v T h u s for (i, j, ~) along an edge of colour \. k s asfai:J is equal to the n u m b e r k Thus of paths of colour under the condition that the first and the third vertices are connected by an edge of colour k aij ~. a >3'-4 s fixed, the product evidently the n u m b e r s J s. Summing over s one obtains k s k aij ~ = ~saijas~. O n the other hand, one can consider paths of colour edge of colour k and then paths of colour this case one obtains expressions cZ. fj w e obtain (j, ~) along an edge of colour (see figure above).

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Advanced paper aicraft construction by Morris


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