On symmetric incidence matrices of projective planes

Autor:	Partha Pratim Dey, J. L. Hayden
Rok vydání:	1995
Předmět:	Combinatorics Character (mathematics) Group (mathematics) Applied Mathematics Incidence matrix Projective plane Abelian group Permutation matrix Square (algebra) Computer Science Applications Mathematics Incidence (geometry)
Zdroj:	Designs, Codes and Cryptography. 6:179-188
ISSN:	1573-7586 0925-1022
Popis:	We investigate the incidence matrix of a finite plane of ordern which admits a (C, L)-transitivityG. The elation groupG affords a generalized Hadamard matrixH=(h ij ) of ordern and an incidence matrix for the plane is completely determined by the matrixR(H)=(R(h ij )), whereR(g) denotes the regular permutation matrix forg∈G. We prove that in the caseR(H) is symmetric thatG is an elementary abelian 2-group or elseG is a nonabelian group andn is a square. Results are obtained in the abelian case linking the roots of the incidence matrixR(H) to the roots of the complex matrix χ(H), χ a nontrivial character ofG.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a7fedd641a1884761fb4e9d82ff892a8 https://doi.org/10.1007/bf01388473 Zobrazit plný text záznamu Full text from SpringerLink