On step-2 transforms for simple perfect squared squares

Simple Perfect Squared Squares and 2 × 1 Squared Rectangles of Orders 21 to 24

Simple perfect squared squares and 2 * 1 squared rectangles of order 26

In this note tables of all simple perfect squared squares and simple 2 × 1 perfect squared rectangles of order 26 are presented.

Simple perfect squared square of lowest order

This note is to report the existence of a simple perfect dissection of a square into 21 unequal squares.

Perfect Matchings and Perfect Squares

In 1961, P.W. Kasteleyn enumerated the domino tilings of a 2n × 2n chessboard. His answer was always a square or double a square (we call such a number "squarish"), but he did not provide a combinatorial explanation for this. In the present thesis, we prove by mostly combinatorial arguments that the number of matchings of a large class of graphs with 4-fold rotational symmetry is squarish; our ...

Perfect Secret Sharing Schemes Based on Generalized Kirkman Squares

Many mathematical structures have been used to model Secret Sharing Schemes. This paper firstly presents a secret sharing schemes based on starter-adder sets of generalized Kirkman squares. Finally, we prove that the scheme is perfect.