$\parbox{7cm}{ {\Huge\bf SEMINARIUM}}$
Zakładu Matematyki Dyskretnej
Wydziału Matematyki Stosowanej
AGH

We wtorek, 20 maja 2003 roku, o godzinie 12:45

w sali 304, łącznik A-3-A-4, A G H

Ingrid SEMANIŠINOVÁ

(Uniwersytet im. Szafarika, Koszyce)

wygłosi referat pod tytułem:

From Latin squares to magic cubes

Latin and magic squares have attracted people for centuries. They were associated with mysticism and magic. From mathematical point of view they provide a number of interesting combinatorial problems that were open for very long time. On the other hand, they provide a suitable material for an improvement of teaching of mathematics at elementary schools and secondary grammar schools.Let $n$ be a positive integer. Latin square is a square table of order $n$ filled with numbers $1,2,\dots, n$ such that each number $1,2,\dots, n$ appears in each row and each column exactly ones. Magic square is a square table of order $n$ filled with numbers $1,2,\dots, n^2$ such that each number appears in the the table exactly ones and the sums of numbers in each row, each column and each diagonal are the same. Magic cube is an analogy of magic square in 3-dimensional space.We present a utilization of orthogonal Latin squares for constructions of magic squares and magic cubes of prescribed orders. These constructions allow us to answer some existential questions concerning magic squares and cubes. Some other generalizations of magic squares will be presented as well.

Serdecznie zapraszamy wszystkich chętnych !