Related papers: Some combinatorial problems arising in the dimer m…
Enumeration of tilings is the mathematical study concerning the total number of coverings of regions by similar pieces without gaps or overlaps. Enumeration of tilings has become a vibrant subfield of combinatorics with connections and…
We study a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure. Particular solutions arise from orthogonal projections of regular polytopes,…
This is a book on higher-categorical diagrams, including pasting diagrams. It aims to provide a thorough and modern reference on the subject, collecting, revisiting and expanding results scattered across the literature, informed by recent…
We discuss some open problems in a program of constructing and studying two-dimensional conformal field theories using the representation theory of vertex operator algebras.
This expository article outlines the construction of De Concini-Procesi arrangement models and describes recent progress in understanding their significance from the algebraic, geometric, and combinatorial point of view. Throughout the…
While the warped extra-dimensional models provide an attractive solution to both the gauge and the flavor hierarchy problems, the mass scale of new particles predicted by the minimal models would be beyond the reach of the LHC. Models of…
We survey recent results on combinatorial optimization problems in which the objective function is the entropy of a discrete distribution. These include the minimum entropy set cover, minimum entropy orientation, and minimum entropy…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
In this paper we provide a framework for the study of isoperimetric problems in finitely generated group, through a combinatorial study of universal covers of compact simplicial complexes. We show that, when estimating filling functions,…
This methodological note investigates and discuss possible selection and collider restriction bias due to predictor availability in prognostic models.
This note presents a discussion of the algebraic and combinatorial aspects of the theory of pure O-sequences. Various instances where pure O-sequences appear are described. Several open problems that deserve further investigation are also…
Experimental mechanisms that yield the growth of homochiral copolymers over their heterochiral counterparts have been advocated by Lahav and co-workers. These chiral amplification mechanisms proceed through racemic {\beta}-sheet-controlled…
Lipid membranes have complex compositions and modeling the thermodynamic properties of multi-component lipid systems remains a remote goal. In this work we attempt to describe the thermodynamics of binary lipid mixtures by mapping…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
We provide a concise exposition with original proofs of combinatorial formulas for the 2D Ising model partition function, multi-point fermionic observables, spin and energy density correlations, for general graphs and interaction constants,…
Many packing, scheduling and covering problems that were previously considered by computer science literature in the context of various transportation and production problems, appear also suitable for describing and modeling various…
We study the behavior of a dimer model under the operation of removing a corner from the lattice polygon and taking the convex hull of the rest. This refines an operation of Gulotta, and the special McKay correspondence plays an essential…
We study a one-dimensional ordinary differential equation modelling optical conveyor belts, showing in particular cases of physical interest that periodic solutions exist. Moreover, under rather general assumptions it is proved that the set…
This is a draft of an article to appear in the October 2022 issue of the Notices of the AMS. In this survey article we explore a fascinating area called descriptive combinatorics and its recently discovered connections to distributed…
This paper contains a selection, dictated by personal taste and by no means complete, of open problems in local discrete holomorphic dynamics.