The Riemann-Roch theorem on a graph G is closely related to Alexander duality in combinatorial commutive algebra. We study the lattice ideal given by chip firing on G and the initial ideal whose standard monomials are the G-parking functions. When G is a saturated graph, these ideals are generic and the Scarf complex is a minimal free resolution. Otherwise, syzygies are obtained by degeneration...

In this talk, we introduce Hilbert functions of a graded algebras over a field, and one of the long standing conjectures concerning them, Fröberg conjecture. Then we study relations between Fröberg conjecture on Hilbert series and Moreno-Socias Conjecture. Consequently, we show that Fröberg conjecture holds for special cases as an example. 1. Almost Reverse Lexicographic Monomial Ideal Let R = ...

this descriptive correlational research sought to examine generic competencies required for university graduates from the points of view of agricultural engineers and mangers in kermanshah province. the study concentrated on the population of public agricultural managers (n= 130) as well as agricultural engineers (who were members of agricultural engineering system organization) in kermanshah p...

We study the initial ideal of binomial edge ideal in degree 2 ([in<(JG)]2), associated to a graph G. We computed dimension, depth, Castelnuovo-Mumford regularity, Hilbert function and Betti numbers of [in<(JG)]2 for some classes of graphs. AMS Mathematics Subject Classification (2010): 05E40, 16E30

We define the monomial invariants of a projective variety Z; they are invariants coming from the generic initial ideal of Z. Using this notion, we generalize a result of Cook [C]: If Z is an integral variety of codimension two, satisfying the additional hypothesis sZ = sΓ, then its monomial invariants are connected.