Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Tatiana Moseeva, St.Petersburg State University, St. Petersburg Department of Steklov Mathematical Institute
Inviter:
Title:	Ambartzumian combinatorial formula and its applications
Language:	English
Time & Venue:	2023.09.01 19:30 - 20:15 N613
Abstract:	Consider a finite set of segments on a plane with endpoints in the general position. In [1] Sylvester posted a problem of finding the measure of the set of lines intersecting all of this segments. In [2] Ambartzumian obtained combinatorial formula that gives an answer to the posted problem. Ambartzumian also gave a combinatorial proof of the Pleijel identity ([3]) by integrating the aforementioned formula. We will discuss proof of Ambartzumian formula and show how it can be used to prove the Pleijel identity. [1] Sylvester, J. J. On a funicular solution of Buffon’s “problem of the needle” in its most general form // Acta Mathematica, 14(1): 185–205, 1890. [2] Ambartzumian, R.V. Combinatorial integral geometry: with applications to mathematical stereology. – John Wiley & Sons – 1982. [3] Pleijel, A. Zwei kurze Beweise der isoperimetrischen Ungleichung. // Archiv der Mathematik, 7(4): 317–319, 1956.