ON HIGHER PARTIAL DERIVATIVES OF IMPLICIT FUNCTIONS AND THEIR COMBINATORICS

Shaul Zemel

doi:10.61091/ojac-1806

ON HIGHER PARTIAL DERIVATIVES OF IMPLICIT FUNCTIONS AND THEIR COMBINATORICS

Shaul Zemel

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a scalar-valued implicit function of many variables, and provide two closed formulae for all of its partial derivatives. One formula is based on products of partial derivatives of the defining function, the other one involves fewer products of building blocks of multinomial type, and we study the combinatorics of the coefficients showing up in both formulae.

Original language	English
Article number	06
Journal	Online Journal of Analytic Combinatorics
Issue number	18
DOIs	https://doi.org/10.61091/ojac-1806
State	Published - 2023

Keywords

Combinatorial Coefficients
Higher Partial Derivatives
Implicit Functions

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.61091/ojac-1806

Cite this

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title = "ON HIGHER PARTIAL DERIVATIVES OF IMPLICIT FUNCTIONS AND THEIR COMBINATORICS",

abstract = "We consider a scalar-valued implicit function of many variables, and provide two closed formulae for all of its partial derivatives. One formula is based on products of partial derivatives of the defining function, the other one involves fewer products of building blocks of multinomial type, and we study the combinatorics of the coefficients showing up in both formulae.",

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AB - We consider a scalar-valued implicit function of many variables, and provide two closed formulae for all of its partial derivatives. One formula is based on products of partial derivatives of the defining function, the other one involves fewer products of building blocks of multinomial type, and we study the combinatorics of the coefficients showing up in both formulae.

KW - Combinatorial Coefficients

KW - Higher Partial Derivatives

KW - Implicit Functions

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U2 - 10.61091/ojac-1806

DO - 10.61091/ojac-1806

M3 - مقالة

SN - 1931-3365

JO - Online Journal of Analytic Combinatorics

JF - Online Journal of Analytic Combinatorics

IS - 18

M1 - 06

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ON HIGHER PARTIAL DERIVATIVES OF IMPLICIT FUNCTIONS AND THEIR COMBINATORICS

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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