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Information Seminar Paper

Title

ON LATTICE BASIS IDEALS OF DIGRAPHS

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Abstract

 LET G BE A DIRECTED GRAPH WITH N VERTICES AND M EDGES, AND I (B) A BINOMIAL IDEAL CORRESPONDED TO THE INCIDENCE MATRIX B OF THE GRAPH G. ALSO BY REMOVING THE I’TH ROW OF B, A NEW MATRIX IS MADE AND IS CALLED BI. IN THIS PAPER IT IS SHOWN THAT THE HEIGHTS OF I (B) AND I (BI) ARE EQUAL TO N-1 AND THE DIMENSIONS OF I (B) AND I (BI) ARE EQUAL TO M-N+1. THEN A SUFFICIENT AND NECESSARY CONDITION IS GIVEN FOR I (BI) TO BE PRIME. A SUFFICIENT COMBINATORIAL CONDITION IS GIVEN FOR I (B) AND I (BI) TO BE COMPLETE INTERSECTIONS. FINALLY A FREE COMPLEX FOR I (B) WILL BE PRESENTED AND, FOR SPECIFIC GRAPHS, A FREE RESOLUTION WILL BE STATED FOR I (B).

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