Matchings from a set below to a set above

Functions from a Set to a Set

The article is a continuation of [1]. We define the following concepts: a function from a set X into a set Y , denoted by “Function of X ,Y ”, the set of all functions from a set X into a set Y , denoted by Funcs(X ,Y ), and the permutation of a set (mode Permutation of X , where X is a set). Theorems and schemes included in the article are reformulations of the theorems of [1] in the new termi...

A RELATION BETWEEN THE CATEGORIES Set * , SetT, Set AND SetT

In this article, we have shown, for the add-point monad T, thepartial morphism category Set*is isomorphic to the Kleisli category SetT. Alsowe have proved that the category, SetT, of T-algebras is isomorphic to thecategory Set of pointed sets. Finally we have established commutative squaresinvolving these categories.

From Elements to a Set

A major index for matchings and set partitions

We introduce a statistic pmaj(P ) for partitions of [n], and show that it is equidistributed with cr2, the number of 2-crossings, over all partitions of [n] with given sets of minimal block elements and maximal block elements. This generalizes the classical result of equidistribution for the permutation statistics inv and maj. © 2007 Elsevier Inc. All rights reserved.

Packing Plane Perfect Matchings into a Point Set

Let P be a set of n points in general position in the plane (no three points on a line). A geometric graph G = (P,E) is a graph whose vertex set is P and whose edge set E is a set of straight-line segments with endpoints in P . We say that two edges of G cross each other if they have a point in common that is interior to both edges. Two edges are disjoint if they have no point in common. A subg...