$k$-congruence orders for $E\sb{k}$

Scissors Congruence for Certain k-polygons

It has been proved that any two polygons having the same area are scissors congruent by Bolyai in 1832 and by Gerwien in 1833, respectively. It is well known that the concepts of congruence and scissors congruence are different for the set of polygons in the Euclidean plane. Let C be a unit circle divided into n parts equally. We denote the set of ends of these parts on C by S = {P0, P1, . . . ...

Some Overpartition k-tuple Congruence Properties

Each of the elements of this list is itself a partition, and the numbers in each partition are referred to as parts . As one may clearly deduce, the larger the number, the more partitions it has. Also of note is the fact that is the same as , that is, order is not accounted for. Typically, the parts of a partition are written in nonincreasing order. It is also commonly accepted that the functio...

RAMANUJAN'S FUNCTION r{n)—k CONGRUENCE PROPERTY

Privacy in Elections: k-Anonymizing Preference Orders

We study the (parameterized) complexity of a combinatorial problem, motivated by the desire to publish elections-related data, while preserving the privacy of the voters (humans or agents). In this problem, introduced and defined here, we are given an election, a voting rule, and a distance function over elections. The task is to find an election which is not too far away from the original elec...

Canonical Forms for Unitary Congruence and *Congruence

We use methods of the general theory of congruence and *congruence for complex matrices—regularization and cosquares—to determine a unitary congruence canonical form (respectively, a unitary *congruence canonical form) for complex matrices A such that ĀA (respectively, A) is normal. As special cases of our canonical forms, we obtain—in a coherent and systematic way—known canonical forms for con...