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In this paper, we present an unexpected link between the Factorial Conjecture ([8]) and Furter’s Rigidity Conjecture ([13]). The Factorial Conjecture in dimension m asserts that if a polynomial f in m variables Xi over C is such that L(f) = 0 for all k ≥ 1, then f = 0, where L is the C-linear map from C[X1, · · · , Xm] to C defined by L(X l1 1 · · ·X lm m ) = l1! · · · lm!. The Rigidity Conject...

We introduce 2-partitionable clutters as the simplest case of the class of kpartitionable clutters and study some of their combinatorial properties. In particular, we study properties of the rank of the incidence matrix of these clutters and properties of their minors. A well known conjecture of Conforti and Cornuéjols [1, 2] states: That all the clutters with the packing property have the max-...

Article history: Received 4 December 2015 Available online 2 August 2016

in this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable taylor and weight function approximation. the method is based on weerakoon-fernando method [s. weerakoon, g.i. fernando, a variant of newton's method with third-order convergence, appl. math. lett. 17 (2000) 87-93]. the method is optimal, as it needs three evaluations per ite...

The goal of this paper is first of all to propose a strategy to attack the generalized Hodge conjecture for coniveau 2 complete intersections, and secondly to state a conjecture concerning the cones of effective cycle classes in intermediate dimensions. Our main results show that the generalized Hodge conjecture for coniveau 2 complete intersections would follow from a particular case of this e...

We discuss the role of K3 surfaces in the context of Mercat’s conjecture in higher rank Brill–Noether theory. Using liftings of Koszul classes, we show that Mercat’s conjecture in rank 2 fails for any number of sections and for any gonality stratum along a Noether– Lefschetz divisor inside the locus of curves lying on K3 surfaces. Then we show that Mercat’s conjecture in rank 3 fails even for c...

The Stanley’s Conjecture on Cohen-Macaulay multigraded modules is studied especially in dimension 2. In codimension 2 similar results were obtained by Herzog, Soleyman-Jahan and Yassemi. As a consequence of our results Stanley’s Conjecture holds in 5 variables.