7823

7288

كارشناسي ارشد

رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1391

هشت،[78]ص.: مصور،نمودار

ص.ع.به فارسي و انگليسي

رياضي

ID7288

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Point symmetric 2 structures Massome Nejadahmad m nejadahmad@math iut ac ir 2013 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Sayed Ghahreman Taherian taherian@cc iut ac ir Advisor Dr Amir Hashemi amir hashemi@cc iut ac ir 2010 MSC 51A99 Keywords Net 2 structure symmetric chain structure midpoint AbstractThis thesis is an extension of the work done by Karzel Kosiorek and Matras 19 Let S be a non empty set P S S the product set and let G1 S x x S andG2 x S x S be the sets of generators Then P G1 G2 is a net i e forall p P forall i 1 2 1 X Gi such that p X and if X G1 Y G2 then X Y 1 A subsetC P is called a chain if forall X G1 G2 C X 1 Let C be the set of all chains ofthe net P G1 G2 for a b P let a b c with c a 1 b 2 we will also write ab a b Let P 2 a b P 2 a b a b and if A B C C let AB P P x y with y x 2 B 1 x 1 A 2 and C CC Then C is an involutory antiautomorphism of P mappingeach chain onto a chain and if D C is a further chain then the product C D is an automorphismof P Two distinct chains A B are called orthogonal denoted by A B if A B B We have A B B A A B B A If K C then P G1 G2 K is called chain structure the setKs C C C K K the symmetric stabilizer of K A chain structure P G1 G2 K is calledsymmetric chain structure if forall K K K K K i e if K Ks and symmetric closed if K Ks A chain structure P G1 G2 K is called 2 structure if forall a b P 2 1 K K a b K weset a b K or in other words if P G1 G2 K is an incidence space i e for any two distinctpoints a b P there is exactly one block B G1 G2 K such that a b B If a b P 2 then also ab ba P 2 and we can form the chains a b and M a b ab ba called the diagonalsof the rectangle a b a ab b ba For M M a b we have M a b and therefore we callM a b the midline of a and b For a chain structure P G1 G2 K let K2 denote the set of all pairs of

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