相关论文: Plinths and Pedestals

We enumerate staircases with fixed left and right columns. These objects correspond to ice-configurations, or alternating sign matrices, with fixed top and bottom parts. The resulting partition functions are equal, up to a normalization…

Chirotopes are a common combinatorial abstraction of (planar) point sets. In this paper we investigate decomposition methods for chirotopes, and their application to the problem of counting the number of triangulations supported by a given…

Enumeration of planar lattice walks is a classical topic in combinatorics, at the cross-roads of several domains (e.g., probability, statistical physics, computer science). The aim of this paper is to propose a new approach to obtain some…

We review the stamp folding problem, the number of ways to fold a strip of $n$ stamps, and the related problem of enumerating meander configurations. The study of equivalence classes of foldings and meanders under symmetries allows to…

We introduce a "deformation" of plumbing. We also define a structure of data used in a calculation by computer aid of the crosscap numbers of alternating knots.

We consider a new kind of straight and shifted plane partitions/Young tableaux --- ones whose diagrams are no longer of partition shape, but rather Young diagrams with boxes erased from their upper right ends. We find formulas for the…

This is a survey article on classical groups (over arbitrary division rings) and their geometries.

We give a new proof of a determinant evaluation due to Andrews, which has been used to enumerate cyclically symmetric and descending plane partitions. We also prove some related results, including a q-analogue of Andrews's determinant.

Every body knows that identical regular triangles or squares can tile the whole plane. Many people know that identical regular hexagons can tile the plane properly as well. In fact, even the bees know and use this fact! Is there any other…

We consider a method of construction of self-similar dendrites on a plane and establish main topological and metric properties of resulting class of dendrites.

Measuring device is proposed for determining a linear dimension. The device comprises three associated longitudinally moving parts one of which is a scale. The integer part of the device reading is being taken from the standard millimeter…

Multi-degree splines are piecewise polynomial functions having sections of different degrees. For these splines, we discuss the construction of a B-spline basis by means of integral recurrence relations, extending the class of multi-degree…

The aim of this paper is to obtain a classification of scrolls of genus 0 and 1, which are defined by a one-dimensional family of lines meeting a certain set of linear spaces in ${\bf P}^n$. These ruled surfaces will be called incidence…

The distance to Pleiades remains controversial. There is a simple way to resolve the dispute definitely by measuring the distance to one of its brightest members, Atlas, which is astrometric and spectroscopic binary.

The kinematics of particles and rigid bodies in the plane are investigated up to higher-order accelerations. Discussion of point trajectories leads from higher-order poles to higher-order Bresse circles of the moving plane. Symplectic…

Staircase tableaux are combinatorial objects which appear as key tools in the study of the PASEP physical model. The aim of this work is to show how the discovery of a tree structure in staircase tableaux is a significant feature to derive…

This expository paper discusses some conjectures related to visibility and blockers for sets of points in the plane.

A new class of random spatial tessellations is introduced -- the so-called column tessellations of three-dimensional space. The construction is based on a stationary planar tessellation. Each cell of the spatial tessellation is a prism…

We evaluate the correlation function of the spectral staircase and use it to evaluate the mesoscopic particle number fluctuations in integrable systems.

The floor and ceiling functions appear often in mathematics and manipulating sums involving floors and ceilings is a subtle game. Fortunately, the well-known textbook Concrete Mathematics provides a nice introduction with a number of…