Let t be a positive integer and let L = (l1, . . . , lt) and K = (k1, . . . , kt) be collections of nonnegative integers. A (t, K,L)-factorization of a graph is a decomposition of the graph into factors F1, . . . , Ft such that Fi is ki-regular and at least li-edge-connected. In this paper we apply the technique of amalgamations of graphs to study (t, K,L)factorizations of complete graphs. In p...

We present an explicit construction of the factorization of Seiberg-Witten curves for N = 2 theory with fundamental flavors. We first rederive the exact results for the case of complete factorization, and subsequently derive new results for the case with breaking of gauge symmetry U(Nc) → U(N1)×U(N2). We also show that integrality of periods is necessary and sufficient for factorization in the ...

We consider the block LDL factorizations for symmetric indefinite matrices in the form LBL , where L is unit lower triangular and B is block diagonal with each diagonal block having dimension 1 or 2. The stability of this factorization and its application to solving linear systems has been well-studied in the literature. In this paper we give a condition under which the LBL factorization will r...

In this paper, we show that the necessary and sufficient condition for the existence of an e Sk-factorization of (Cm ◦ Kn)∗ is n ≡ 0 (mod k(k − 1)), for all m > 3. In fact, our result together with a result of Ushio gives a complete solution for the existence of an e Sk-factorization of (Cm ◦Kn)∗ for all m ≥ 3. Further, we have obtained some necessary or sufficient conditions for the existence ...

We continue investigating the superintegrability property of matrix models, i.e. factorization model averages characters. This paper focuses on Gaussian Hermitian example, where role characters is played by Schur functions. find a new intriguing corollary superintegrability: an infinite set correlators bilinear in More exactly, these are products functions and polynomials $K_\Delta$ that form c...

A unified treatment of parameters relevant to factoring polynomials over finite fields is given. The framework is based on generating functions for describing parameters of interest and on singularity analysis for extracting asymptotic values. An outcome is a complete analysis of the standard polynomial factorization chain that is based on elimination of repeated factors, distinct degree factor...

This paper presents a preconditioning method based on combining two-sided permutations with a multilevel approach. The nonsymmetric permutation exploits a greedy strategy to put large entries of the matrix in the diagonal of the upper leading submatrix. The method can be regarded as a complete pivoting version of the incomplete LU factorization. This leads to an effective incomplete factorizati...