Combinatorics of multiboundary singularities Bnl and Bernoulli-Euler numbers
Abstract
Consider generalizations of the boundary singularities Bn of the functions on the real line to the case where the boundary consists of a finite number of l points. These singularities Bnl could also arise in higher dimensional case, when the boundary is an immersed hypersurface. We obtain a particular recurrent equation on the numbers of connected components of very nice M-morsification spaces of the multiboundary singularities Bnl. This helps us to express the numbers Knl (for l=2,3,4...) by Bernoulli-Euler numbers. We also find the corresponding generating functions.
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