We define and study a class of finite topological spaces, which model the cell structure of a space obtained by gluing finitely many Euclidean convex polyhedral cells along congruent faces. We call these finite topological spaces, combinatorial cell complexes (or c.c.c). We define orientability, homology and cohomology of c.c.c’s and develop enough algebraic topology in this setting to prove th...

In this paper we explore whether an auctioneer/buyer may benefit from introducing his transformability relationships (some goods can be transformed into others at a transformation cost) into multi-unit combinatorial reverse auctions. Thus, we quantitatively assess the potential savings the auctioneer/buyer may obtain with respect to combinatorial reverse auctions that do not consider tranformab...

We explore the combinatorial properties of a particular type of extension monoid product of preinjective Kronecker modules. The considered extension monoid product plays an important role in matrix completion problems. We state theorems which characterize this product in both implicit and explicit ways and we prove that the conditions given in the definition of the generalized majorization are ...

It is well known that the duality theory for linear programming (LP) is powerful and elegant and lies behind algorithms such as simplex and interior-point methods. However, the standard Lagrangian for nonlinear programs requires constraint qualifications to avoid duality gaps. Semidefinite linear programming (SDP) is a generalization of LP where the nonnegativity constraints are replaced by a s...

A theorem of Laman gives a combinatorial characterisation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in R. A more general theory is developed for frameworks in R whose vertices are constrained to move on a two-dimensional smooth submanifold M. Furthermore, when M is a union of concentric spheres, or a union of parallel planes or a union of concentric...

In this paper we explore whether an auctioneer/buyer may benefit from introducing his transformability relationships (some goods can be transformed into others at a transformation cost) into multi-unit combinatorial reverse auctions. Thus, we quantitatively assess the potential savings the auctioneer/buyer may obtain with respect to combinatorial reverse auctions that do not consider tranformab...

The notion of k-systolic (k ≥ 6 being a natural number) complexes was introduced by T. Januszkiewicz and J. Świa̧tkowski [JS1] and, independently, by F. Haglund [H] as combinatorial analogue of nonpositively curved spaces. Those complexes are simply connected simplicial complexes satisfying some local combinatorial conditions. Roughly speaking there is a lower bound for the length of “essential"...

the development of multicomponent reactions (mcrs) designed to produce elaborate biologically active compounds has become an important area of research in organic, combinatorial, and medicinal chemistry. a comparative study of the synthesis of new bis-spiro-oxindolo(pyrrolizidines/pyrrolidines) ring systems by the cycloaddition of azomethine ylides generated by a decarboxylative route from sarc...

Many current deterministic solvers for NP-hard combinatorial optimization problems are based on nonlinear relaxation techniques that use floating point arithmetic. Occasionally, due to solving these relaxations, rounding errors may produce erroneous results, although the deterministic algorithm should compute the exact solution in a finite number of steps. This may occur especially if the relax...

We continue our series of papers on the graph theoretic spectral theory of matrices. Let A be an Mmatrix. We introduce the concepts of combinatorial vectors and proper combinatorial vectors in the generalized nuUspacc E(A) of A. \\e explore the properties of combinatorial bases for E(A) and Jordan bases for E(A) derived from proper combinatorial sets of vectors. We use properties of these bases...