Английская Википедия:Ilona Palásti
Шаблон:Short description Ilona Palásti (1924–1991) was a Hungarian mathematician who worked at the Alfréd Rényi Institute of Mathematics. She is known for her research in discrete geometry, geometric probability, and the theory of random graphs.Шаблон:R With Alfréd Rényi and others, she was considered to be one of the members of the Hungarian School of Probability.Шаблон:R
Contributions
In connection to the Erdős distinct distances problem, Palásti studied the existence of point sets for which the <math>i</math>th least frequent distance occurs <math>i</math> times. That is, in such points there is one distance that occurs only once, another distance that occurs exactly two times, a third distance that occurs exactly three times, etc. For instance, three points with this structure must form an isosceles triangle. Any <math>n</math> evenly-spaced points on a line or circular arc also have the same property, but Paul Erdős asked whether this is possible for points in general position (no three on a line, and no four on a circle). Palásti found an eight-point set with this property, and showed that for any number of points between three and eight (inclusive) there is a subset of the hexagonal lattice with this property. Palásti's eight-point example remains the largest known.Шаблон:RШаблон:Ran
Another of Palásti's results in discrete geometry concerns the number of triangular faces in an arrangement of lines. When no three lines may cross at a single point, she and Zoltán Füredi found sets of <math>n</math> lines, subsets of the diagonals of a regular <math>2n</math>-gon, having <math>n(n-3)/3</math> triangles. This remains the best lower bound known for this problem, and differs from the upper bound by only <math>O(n)</math> triangles.Шаблон:RШаблон:Ran
In geometric probability, Palásti is known for her conjecture on random sequential adsorption, also known in the one-dimensional case as "the parking problem". In this problem, one places non-overlapping balls within a given region, one at a time with random locations, until no more can be placed. Palásti conjectured that the average packing density in <math>d</math>-dimensional space could be computed as the <math>d</math>th power of the one-dimensional density.Шаблон:R Although her conjecture led to subsequent research in the same area, it has been shown to be inconsistent with the actual average packing density in dimensions two through four.Шаблон:RШаблон:Ran
Palásti's results in the theory of random graphs include bounds on the probability that a random graph has a Hamiltonian circuit, and on the probability that a random directed graph is strongly connected.Шаблон:RШаблон:RanШаблон:Ran
Selected publications
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References
