相关论文: A generalization of Bressoud's beautiful bijection
This work establishes a characterization theorem for (generalized) Young measures generated by symmetric derivatives of functions of bounded deformation (BD) in the spirit of the classical Kinderlehrer-Pedregal theorem. Our result places…
We describe a bijection between oriented cubes and adjoints of cross-polytopes. This correspondence is used to prove that the real affine cube is, up to reorientation in the same class, the unique oriented cube that is realizable. Moreover,…
There is a classical geometric construction which uses a binary quadratic form to define an involution on the space of binary d-ics. We give a complete characterization of a general class of such involutions which are definable using…
Starting from some considerations we make about the relations between certain difference statistics and the classical permutation statistics we study permutations whose inversion number and excedance difference coincide. It turns out that…
In 1997, Schaeffer described a bijection between Eulerian planar maps and some trees. In this work we generalize his work to a bijection between bicolorable maps on a surface of any fixed genus and some unicellular maps with the same genus.…
In this paper, we survey constructions of and nonexistence results on combinatorial/geometric structures which arise from unions of cyclotomic classes of finite fields. In particular, we survey both classical and recent results on…
In this work we present a general and versatile algorithmic framework for exhaustively generating a large variety of different combinatorial objects, based on encoding them as permutations. This approach provides a unified view on many…
Normal ideals on regular uncountable cardinals are familiar objects. We investigate ideals that are pleasant--while a normal ideal is closed under arbitrary diagonal unions, a pleasant ideal is closed only under diagonal unions indexed by…
The inverse problem of general rough sets, considered by the present author in some of her earlier papers, in one of its manifestations is essentially the question of when an agent's view about crisp and non crisp objects over a set of…
We consider systems of recursively defined combinatorial structures. We give algorithms checking that these systems are well founded, computing generating series and providing numerical values. Our framework is an articulation of the…
In this paper, we survey some properties, encoding, and bijections involving combinatorial maps, double occurrence words, and chord diagrams. We particularly study quasi-trees from a purely combinatorial point of view and derive a…
To each simplicial set $X$ we naturally assign an \'etendue ${\'E X}$ whose internal logic captures information about the geometry of $X$. In particular, we show that, for 'non-singular' objects $X$ and $Y$, the \'etendues ${\'E X}$ and…
We present a simple proof of the well-known fact concerning the number of solutions of diagonal equations over finite fields. In a similar manner, we give an alternative proof of the recent result on generalizations of Carlitz equations. In…
Tree-like tableaux are objects in bijection with alternative or permutation tableaux. They have been the subject of a fruitful combinatorial study for the past few years. In the present work, we define and study a new subclass of tree-like…
In this note we give a simple unifying proof of the undecidability of several diagrammatic properties of term rewriting systems that include: local confluence, strong confluence, diamond property, subcommutative property, and the existence…
We survey structures endowed with natural partial orderings and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism order…
We study the factorizations of the permutation $(1,2,...,n)$ into $k$ factors of given cycle types. Using representation theory, Jackson obtained for each $k$ an elegant formula for counting these factorizations according to the number of…
We define a map between the set of permutations that avoid either the four patterns $3214,3241,4213,4231$ or $3124,3142,4123,4132$, and the set of Dyck prefixes. This map, when restricted to either of the two classes, turns out to be a…
We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and…
A k-triangulation of a convex polygon is a maximal set of diagonals so that no k+1 of them mutually cross in their interiors. We present a bijection between 2-triangulations of a convex n-gon and pairs of non-crossing Dyck paths of length…