Birth date:
14.01.1980
E-mail: Keywords: combinatorics,
singularity theory,
multiboundary singularities,
energies of knots,
variational principles of energies of knots,
many-dimensional continued fractions.
Subject:
1. Consider generalizations of the boundary singularities $B_n$ of the functions on the real line to the case where the boundary consists of a finite number of ($l$) points. These singularities $B_n^l$ could also arise in higher dimensional case, when the boundary is an immersed hypersurface. We obtain some recurrent equation on the numbers of connected components of very nice M-morsification spaces of the multiboundary singularities $B_n^l$. This helps us to express $K_n^l$ numbers (for $l=2, 3, 4, ...$) by Bernoulli–Euler numbers. We also find the corresponding generating functions.
Main publications:
Karpenkov O. N. Kombinatorika multikraevykh osobennostei serii $B_n^l$ i chisla Bernulli–Eilera // Funkts. analiz i ego pril. Prinyato k pechati v 2002.
