This paper is concerned with structures of general graphs with perfect matchings. We first reveal a partially ordered structure among factor-components of general graphs with perfect matchings. Our second result is a generalization of Kotzig’s canonical partition to a decomposition of general graphs with perfect matchings. It contains a short proof for the theorem of the canonical partition. Th...

The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such measures. These are shown to preserve the generalized monodromy of the associated rank-2 rational covariant derivative operators. The corresponding matrix m...

Symplectic modular invariance of the bosonic string partition function has been verified at genus 2 and 3 using the period matrix coordinatization of moduli space. A calculation of the transformation of the holomorphic part of the differential volume element shows that an extra phase arises together with the factor associated with a specific modular weight; the phase is cancelled in the transfo...

First we show that the cosets of a fuzzy ideal μ in a BCK-algebraX form another BCK-algebra  X/μ (called the fuzzy quotient BCK-algebra of X by μ). Also we show thatX/μ is a fuzzy partition of X and we prove several some isomorphism theorems. Moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition P of a commutative BCK-algebra iscompatible, then P is a fuzzy quo...

We analyze the exact partition function of the Ising model on a square lattice under helical boundary conditions obtained by Liaw [Phys. Rev. E 73, 055101(R) (2006)]. Based on such an expression, we then extend the algorithm of Ivashkevich, Izmailian, and Hu [J. Phys. A 35, 5543 (2002)] to derive an exact asymptotic expansion of the logarithm of the partition function and its first to fourth de...

We show that the maximum matroid-greedoid partition problem is NP-hard to approximate to within 1/2 + ε for any ε > 0, which matches the trivial factor 1/2 approximation algorithm. The main tool in our hardness of approximation result is an extractor code with polynomial rate, alphabet size and list size, together with an efficient algorithm for list-decoding. We show that the recent extractor ...

has polynomial time complexity if the integers are supplied in unary radix. We show that if the input is supplied in binary (or higher) radix, then this problem is in #P and is actually the counting version of the Partition problem. We also state additional properties of the Partition problem following our analysis. In particular, we show that deciding whether definite integrals are zero or inf...

We analyse supermembrane instantons (fully wrapped supermembranes) by computing the partition function of the three-dimensional supersymmetrical U(N) matrix model under periodic boundary conditions. By mapping the model to a cohomological field theory and considering a mass-deformation of the model, we show that the partition function exactly leads to the U-duality invariant measure factor ente...

We evaluate quasi-classically the Ramond partition function of Euclidean D = 10 U(N) super-Yang{Mills theory reduced to a two-dimensional torus. The result can be interpreted in terms of free strings wrapping the space-time torus, as expected from the point of view of Matrix string theory. We demonstrate that, when extrapolated to the ultraviolet limit (small area of the torus), the quasi-class...

We evaluate quasiclassically the Ramond partition function of Euclidean D = 10 U(N) super Yang-Mills theory reduced to a two-dimensional torus. The result can be interpreted in terms of free strings wrapping the space-time torus, as expected from the point of view of Matrix string theory. We demonstrate that, when extrapolated to the ultraviolet limit (small area of the torus), the quasiclassic...