TY - JOUR
ID - 4121
TI - On the rank of the holomorphic solutions of PDE associated to directed graphs
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN -
AU - Damadi, Hamid
AU - Rahmati, Farhad
AD - Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
Y1 - 2021
PY - 2021
VL - 2
IS - 1
SP - 1
EP - 9
KW - Directed graph
KW - Binomial D-module
KW - Lattice basis ideal
DO - 10.22060/ajmc.2020.18413.1031
N2 - Let G be a directed graph with m vertices and n edges, I(B) thebinomial ideal associated to the incidence matrix B of the graph G, and I_L the latticeideal associated to the columns of the matrix B. Also let B_i be a submatrix ofB after removing the ith column. In this paper it is determined that which primeminimal ideals of I(B_i) are Andean or toral. Then we study the rank of the spaceof solutions of binomial D-module associated to I(B_i) as A-graded ideal, where A isa matrix that, AB_i = 0. Afterwards, we define a maximal cellular cycle and provethat for computing this rank it is enough to consider these components of G. Weintroduce some bounds for the number of the vertices of the convex hull generatedby the columns of the matrix A. Finally an algorthim is introduced by which we cancompute the volume of the convex hull corresponded to a cycles with k diagonals, soby Theorem 2.1 the rank of (D / H_A(I(B_i); beta)) can be computed.
UR - https://ajmc.aut.ac.ir/article_4121.html
L1 - https://ajmc.aut.ac.ir/article_4121_93e1173b7519f0c5363021779bf5afe9.pdf
ER -