The canonical coding partition of a set of words is the finest partition such that the words contained in at least two factorizations of a same sequence belong to a same class. In the case the set is not uniquely decipherable, it partitions the set into one unambiguous class and other parts that localize the ambiguities in the factorizations of finite sequences. We prove that the canonical codi...

Motivated by the study of decipherability conditions for codes weaker than Unique Decipherability (UD), we introduce the notion of coding partition. Such a notion generalizes that of UD code and, for codes that are not UD, allows to recover the “unique decipherability” at the level of the classes of the partition. By tacking into account the natural order between the partitions, we define the c...

By working in a symplectically covariant real formulation of special K\"ahler geometry, we propose and give strong evidence for canonical BPS partition function AdS$_2 \times_w M_2$ near-horizon geometries with arbitrary rotation generic magnetic electric charges. Here, $M_2$ is either two-sphere or spindle. We also show that how the attractor equations Bekenstein-Hawking entropy can be obtaine...

A simple method to obtain a canonical partition function for a one-dimensional lattice gas model is presented. The simplification is based upon rewriting a sum over all possible configurations as a sum over all possible numbers of clusters in the system.

A canonical (i.e., unrestricted) version of the partition theorem for k-parameter sets of Graham and Rothschild (Trans. Amer. Math. Sot. 159 (1971), 257-291) is proven. Some applications, e.g., canonical versions. of the Rado-Folkman-Sanders theorem and of the partition theorem for finite Boolean algebras are given. Also the ErdBs-Rado canonization theorem (J. London Math. Sot. 25 (1950), 249-2...

It has been recently pointed out that a definition of the geometric entropy using the partition function in a conical space does not in general lead to a positive definite quantity. For a scalar field model with a non-minimal coupling we clarify the origin of the anomalous behavior from the viewpoint of the canonical formulation.

From the partition function of canonical ensemble we derive the entropy of the de Sitter space by anti-Wick rotation. And then from the one-loop bubble S 2 × S 2 created from vacuum fluctuation in de Sitter background space, we obtain the one-loop quantum correction to the entropy of de Sitter space.

We consider the effective topological field theory on Euclidean D-strings wrapping on a 2cycle in the internal space. We evaluate the vev of a suitable operator corresponding to the chemical potential of vortices bounded to the D-strings, and find that it reduces to the partition function of generalized two-dimensional Yang-Mills theory as a result of localization. We argue that the partition f...

We consider the effective topological field theory on Euclidean D-strings wrapping on a 2-cycle in the internal space. We evaluate the vev of an appropriate operator corresponding to the chemical potential of D-instantons bounded to the D-strings, and find that it reduces to the partition function of generalized two-dimensional Yang-Mills theory as a result of localization. We argue that the pa...

We calculate the partition functions of QCD in two dimensions on a cylinder and on a torus in the gauge ∂ 0 A 0 = 0 by integrating explicitly over the non zero modes of the Fourier expansion in the periodic time variable. The result is a one dimensional Kazakov-Migdal matrix model with eigenvalues on a circle rather than on a line. We prove that our result coincides with the standard expansion ...