Bernoulli-Euler updown numbers associated with function singularities, their combinatorics and arithmetics

DOI10.1215/S0012-7094-91-06323-4zbMath0755.58015OpenAlexW1513933284WikidataQ56039765 ScholiaQ56039765MaRDI QIDQ1179179

Vladimir I. Arnold

Publication date: 26 June 1992

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-91-06323-4

zbMATH Keywords

critical pointssmooth functionstopologically different maximal morsifications

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Singularities of differentiable mappings in differential topology (57R45)

Related Items (17)

Number of components of the set of real morsifications of \(D_ \mu\) singularities ⋮ The Entringer-Poupard matrix sequence ⋮ Up-down coefficients for permutations ⋮ On arithmetic and asymptotic properties of up-down numbers ⋮ Enumeration formulas for Young tableaux in a diagonal strip ⋮ On the number of connected components in the space of M-polynomials in hyperbolic functions ⋮ On distribution of the number of peaks and the Euler numbers of permutations ⋮ Modular periodicity of the Euler numbers and a sequence by Arnold ⋮ Moduli spaces of Morse functions for persistence ⋮ The free tangent law ⋮ Efficient computation of Favard constants and their connection to Euler polynomials and numbers ⋮ Topological classification of trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges ⋮ On Appell sequences of polynomials of Bernoulli and Euler type ⋮ Zigzags with Bürgi, Bernoulli, Euler and the Seidel-Entringer-Arnol'd triangle ⋮ A Bose type formula for the internal medial axis of an embedded manifold ⋮ On the number of connected components of the space of trigonometric polynomials of degree \(n\) with \(2n\) different critical values ⋮ Periodic de Bruijn triangles: exact and asymptotic results

Cites Work

• Computation of Tangent, Euler, and Bernoulli Numbers
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