{"product_id":"9789814651097","title":"Geometry Of Semilinear Embeddings: Relations To Graphs And Codes: Relations to Graphs and Codes","description":"\u003cp\u003eThis volume covers semilinear embeddings of vector spaces over division rings and the associated mappings of Grassmannians. In contrast to classical books, we consider a more general class of semilinear mappings and show that this class is important. A large portion of the material will be formulated in terms of graph theory, that is, Grassmann graphs, graph embeddings, and isometric embeddings. In addition, some relations to linear codes will be described. Graduate students and researchers will find this volume to be self-contained with many examples.\u003c\/p\u003e\u003cb\u003eContents:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eSemilinear Mappings:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eDivision Rings and Their Homomorphisms\u003c\/li\u003e\n\u003cli\u003eVector Spaces Over Division Rings\u003c\/li\u003e\n\u003cli\u003eSemilinear Mappings\u003c\/li\u003e\n\u003cli\u003eSemilinear Embeddings\u003c\/li\u003e\n\u003cli\u003eMappings of Grassmannians Induced by Semilinear Embeddings\u003c\/li\u003e\n\u003cli\u003eKreuzer's Example\u003c\/li\u003e\n\u003cli\u003eDuality\u003c\/li\u003e\n\u003cli\u003eCharacterization of Strong Semilinear Embeddings\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eProjective Geometry and Linear Codes:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eProjective Spaces\u003c\/li\u003e\n\u003cli\u003eFundamental Theorem of Projective Geometry\u003c\/li\u003e\n\u003cli\u003eProof of Theorem 1.2\u003c\/li\u003e\n\u003cli\u003e\n\u003ci\u003em\u003c\/i\u003e-independent Subsets in Projective Spaces\u003c\/li\u003e\n\u003cli\u003ePGL-subsets\u003c\/li\u003e\n\u003cli\u003eGeneralized MacWilliams Theorem\u003c\/li\u003e\n\u003cli\u003eLinear Codes\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eIsometric Embeddings of Grassmann Graphs:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eGraph Theory\u003c\/li\u003e\n\u003cli\u003eElementary Properties of Grassmann Graphs\u003c\/li\u003e\n\u003cli\u003eEmbeddings\u003c\/li\u003e\n\u003cli\u003eIsometric Embeddings\u003c\/li\u003e\n\u003cli\u003eProof of Theorem 3.1\u003c\/li\u003e\n\u003cli\u003eEquivalence of Isometric Embeddings\u003c\/li\u003e\n\u003cli\u003eLinearly Rigid Isometric Embeddings\u003c\/li\u003e\n\u003cli\u003eRemarks on Non-isometric Embeddings\u003c\/li\u003e\n\u003cli\u003eSome Results Related to Chow's Theorem\u003c\/li\u003e\n\u003cli\u003eHuang's Theorem\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eJohnson Graph in Grassmann Graph:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eJohnson Graph\u003c\/li\u003e\n\u003cli\u003eIsometric Embeddings of Johnson Graphs in Grassmann Graphs\u003c\/li\u003e\n\u003cli\u003eProof of Theorem 4.2\u003c\/li\u003e\n\u003cli\u003eClassification Problem and Relations to Linear Codes\u003c\/li\u003e\n\u003cli\u003eCharacterizations of Apartments in Building Grassmannians\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eCharacterization of Isometric Embeddings:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eMain Result, Corollaries and Remarks\u003c\/li\u003e\n\u003cli\u003eCharacterization of Distance\u003c\/li\u003e\n\u003cli\u003eConnectedness of the Apartment Graph\u003c\/li\u003e\n\u003cli\u003eIntersections of \u003ci\u003eJ\u003c\/i\u003e(\u003ci\u003en, k\u003c\/i\u003e)-subsets of Different Types\u003c\/li\u003e\n\u003cli\u003eProof of Theorem 5.1\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eSemilinear Mappings of Exterior Powers:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eExterior Powers\u003c\/li\u003e\n\u003cli\u003eGrassmannians\u003c\/li\u003e\n\u003cli\u003eGrassmann Codes\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003e\u003cb\u003eReadership:\u003c\/b\u003e Graduate students and researchers interested in the field of semilinear embeddings.\u003cbr\u003e","brand":"World Scientific Publishing Company, Incorporated","offers":[{"title":"Default Title","offer_id":47139929784560,"sku":"9789814651097","price":22.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9789814651097_p0.jpg?v=1763692636","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9789814651097","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}