Related papers: Sparse Versions of the Cayley-Bacharach Theorem
We give an elementary, self-contained, and purely combinatorial proof of the Rayleigh monotonicity property of graphs.
Chiral perturbation theory is a very general expansion method which can be applied to any dynamical system which has continuous global symmetries and in which the ground state breaks some of these spontaneously. In these lectures we explain…
Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues…
We offer streamlined proofs of fundamental theorems regarding the index theory for partial self-maps of an infinite set that are bijective between cofinite subsets.
An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…
In this note, we simplify the statements of theorems attributed to Cauchy and Ostrovsky and give proofs of each theorem via combinatorial and nonnegative matrix theory. We also show that each simple sufficient condition in each statement is…
We establish a new simple explicit description of combinatorial wall-crossing for the rational Cherednik algebra applied to the trivial representation. In this way we recover a theorem of P. Dimakis and G. Yue. We also present two…
The recent two proofs for the (weak) factorization theorem for birational maps, one by W{\l}odarczyk and the other by Abramovich-Karu-Matsuki-W{\l}odarczyk rely on the results of Morelli. The former uses the process for…
We describe a bigraded generalization of the Weil algebra, of its basis and of the characteristic homomorphism which besides ordinary characteristic classes also maps on Donaldson invariants.
We prove several results from different areas of extremal combinatorics, giving complete or partial solutions to a number of open problems. These results, coming from areas such as extremal graph theory, Ramsey theory and additive…
The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These…
We present several direct bijections between different combinatorial interpretations of the Littlewood-Richardson coefficients. The bijections are defined by explicit linear maps which have other applications.
We give an analytic version of the injectivity theorem by using multiplier ideal sheaves, and prove some extension theorems for the adjoint bundle of dlt pairs. Moreover, by combining techniques of the minimal model program, we obtain some…
We identify and study a simple combinatorial problem that is derived from submodularity issues encountered in the theory of tangles of graphs and abstract separation systems.
We generalize Gassert-Shor formula for numerical semigroups.
Sparse Gaussian processes and various extensions thereof are enabled through inducing points, that simultaneously bottleneck the predictive capacity and act as the main contributor towards model complexity. However, the number of inducing…
We study the generalized double $\beta$-Grothendieck polynomials for all types. We study the Cauchy formulas for them. Using this, we deduce the K-theoretic version of the comodule structure map $\alpha^*: K(G/B)\to K(G)\otimes K(G/B)$…
In this article we use existing machinery to define connective $K$-theory spectra associated to topological ringoids. Algebraic $K$-theory of discrete ringoids, and the analytic $K$-theory of Banach categories are obtained as special cases.…
We consider the problem of enumeration of planar maps and revisit its one-matrix model solution in the light of recent combinatorial techniques involving conjugated trees. We adapt and generalize these techniques so as to give an…
It is shown here that a strengthening of Wallach's Unentangled Gleason Theorem can be obtained by applying results of the present authors on generalised Gleason theorems for quantum multi-measures arising from investigations of quantum…