We consider maps on genus-$g$ surfaces with $n$ (labeled) faces of prescribed even degrees. It is known since work Norbury that, if one disallows vertices degree one, the enumeration such related to counting lattice point in moduli space curves labeled points and given by a symmetric polynomial $N_{g,n}(\ell_1,\ldots,\ell_n)$ face degrees $2\ell_1, \ldots, 2\ell_n$. generalize this restricting ...

The correspondence between perfect difference sets and transitive projective planes is well-known. We observe that all known dense (i.e., close to square-root size) Sidon subsets of abelian groups come from through a similar construction. classify the arising in this manner desarguesian find essentially no new examples, but there are many further examples nondesarguesian planes. conjecture aris...

This paper is the first in a series where we attempt to define defects critical lattice models that give rise conformal field theory topological continuum limit. We focus mostly on based Temperley-Lieb algebra, with future applications restricted solid-on-solid (also called anyonic chains) models, as well non-unitary like percolation or self-avoiding walks. Our approach essentially algebraic an...

The categorical dualities presented are: (first) for the category of bi-algebraic lattices that belong to variety generated by smallest non-modular lattice with complete (0,1)-lattice homomorphisms as morphisms, and (second) non-trivial (0,1)-lattices belonging same morphisms. Although two categories coincide on their finite objects, essentially differ mostly but not only fact duality second us...

Model theory, a branch of mathematical logic which involves the study of sets definable in a mathematical structure using an appropriate first order language, has recently shown its capacity to produce applications to other domains of mathematics, principally to algebra, algebraic geometry and number theory. The main example is the proof by Ehud Hrushovski of a conjecture of algebraic geometry,...

Model-driven engineering (MDE) is a prominent approach to software development, in which models of the domain and the software system are primary assets of the development process. Normally, models are inter-related, perhaps in a very complex way, and keeping them mutually consistent (synchronized) is a difficult task, which is crucial for MDE. An important special case is synchronization of tw...

We show that two essentially conditional linear information inequalities (including the Zhang–Yeung’97 conditional inequality) do not hold for asymptotically entropic points. This result raises the question of the “physical” meaning of these inequalities and the validity of their use in practice-oriented applications.