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Combinatorics of multiboundary singularities B_n^l and Bernoulli-Euler numbers

Oleg Karpenkov
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Abstract

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 a particular 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 the numbers K_n^l (for l=2,3,4...) by Bernoulli-Euler numbers. We also find the corresponding generating functions.

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Oleg Karpenkov. 2006-04-03. Combinatorics of multiboundary singularities B_n^l and Bernoulli-Euler numbers. https://arxiv.org/abs/math/0604024

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