ON LATTICE IDEALS AND LATTICE BASIS IDEALS ASSOCIATED TO ORIENTED GRAPHS

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Damadi Hamid; RAHMATI FARHAD

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Journal Paper

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Journal: TRANSACTIONS ON COMBINATORICS Year:2018 | Volume:7 | Issue:2 Page(s): 35-46

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Information Journal Paper

Title

ON LATTICE IDEALS AND LATTICE BASIS IDEALS ASSOCIATED TO ORIENTED GRAPHS

Author(s)

Damadi Hamid | RAHMATI FARHAD | Issue Writer Certificate

Keywords

DIRECTED GRAPH

BINOMIAL IDEAL

MATRIX IDEALS

Abstract

Let G be a simple, oriented connected graph with n vertices and m edges. Let I (B) be the BINOMIAL IDEAL associated to the incidence matrix B of the graph G. Assume that IL is the lattice ideal associated to the rows of the matrix B. Also let Bi be a sub matrix of B after removing the i -th row. We introduce a graph theoretical criterion for G which is a sufficient and necessary condition for I (B) =I (Bi) and I (Bi) =IL. After that we introduce another graph theoretical criterion for G which is a sufficient and necessary condition for I (B) =IL. 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 I (Bi) is a complete intersection ideal.

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APA: Copy

Damadi, Hamid, & RAHMATI, FARHAD. (2018). ON LATTICE IDEALS AND LATTICE BASIS IDEALS ASSOCIATED TO ORIENTED GRAPHS. TRANSACTIONS ON COMBINATORICS, 7(2), 35-46. SID. https://sid.ir/paper/714585/en

Vancouver: Copy

Damadi Hamid, RAHMATI FARHAD. ON LATTICE IDEALS AND LATTICE BASIS IDEALS ASSOCIATED TO ORIENTED GRAPHS. TRANSACTIONS ON COMBINATORICS[Internet]. 2018;7(2):35-46. Available from: https://sid.ir/paper/714585/en

IEEE: Copy

Hamid Damadi, and FARHAD RAHMATI, “ON LATTICE IDEALS AND LATTICE BASIS IDEALS ASSOCIATED TO ORIENTED GRAPHS,” TRANSACTIONS ON COMBINATORICS, vol. 7, no. 2, pp. 35–46, 2018, [Online]. Available: https://sid.ir/paper/714585/en

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