Cover Image

A new simple proof of cayles’s formula and its relationship with the Kirkwood – Salzburg equations

UDC 519.1 A new very simple proof of the formula for the number of labeled root forest-graphs with a given number of vertices is proposed.&nbsp;As a partial case of this formula, we obtain Cayley's formula.

Saved in:

Bibliographic Details
Date:	2022
Main Authors:	Rebenko, O. L., Rebenko, Alexei, Ребенко, О. Л.
Format:	Article
Language:	Ukrainian
Published:	Institute of Mathematics, NAS of Ukraine 2022
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/7156
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
Download file:

Institution

Ukrains’kyi Matematychnyi Zhurnal

Similar Items

A new simple proof of Cayles&#039;s formula and its relationship with the Kirkwood–Salzburg equations
by: O. L. Rebenko
Published: (2022)

Kirkwood–Salzburg equation for connected correlation functions
by: Rebenko, O., et al.
Published: (2026)

On the relations between some approaches to solving the Kirkwood – Salzburg equations
by: Rebenko, A. L., et al.
Published: (2021)

On the relations between some approaches to solving the Kirkwood – Salzburg equations
by: O. L. Rebenko
Published: (2021)

A Simple Proof of Sklyanin's Formula for Canonical Spectral Coordinates of the Rational Calogero-Moser System
by: Görbe, T.F.
Published: (2016)

On virial expansions of correlation functions. Canonical ensemble
by: Pogorelov, Yu., et al.
Published: (2023)

On lattice oscillator-type Kirkwood - Salsburg equation with attractive manybody potentials
by: Skrypnik, W. I., et al.
Published: (2010)

Solutions of the Kirkwood-Salsburg equation for particles with finite-range nonpairwise repulsion
by: Skrypnik, W. I., et al.
Published: (2008)

A simplified proof of the reduction point crossing sign formula for Verma modules
by: Denis, M.St., et al.
Published: (2019)

On the lattice oscillator-type Kirkwood–Salsburg equation with attractive many-body potentials
by: Skrypnik, W.I.
Published: (2010)

A simple proof of the Radó and Král theorems on removability of the zero locus for analytic and harmonic functions
by: Pokrovskii, A.V.
Published: (2015)

Kirkwood–Salsburg equation for a quantum lattice system of oscillators with many-particle interaction potentials
by: Skrypnik, W. I., et al.
Published: (2009)

A new proof of Frank-Weissenborn inequality
by: Gol`dberg, A.
Published: (2005)

On a new form of the Mayer expansion
by: O. L. Rebenko, et al.
Published: (2015)

Exact Formulas of the Transition Probabilities of the Multi-Species Asymmetric Simple Exclusion Process
by: Lee, Eunghyun
Published: (2020)

A Constructive Proof for the Umemura Polynomials of the Third Painlevé Equation
by: Clarkson, Peter A., et al.
Published: (2023)

A simple parsimony-based approach to assess ancestor-descendant relationships
by: Aubert, D.
Published: (2017)

A simple proof of the Radґo and Krґal theorems on removability of the zero locus for analytic and harmonic functions
by: A. V. Pokrovskii
Published: (2015)

A New (But Very Nearly Old) Proof of the Rogers-Ramanujan Identities
by: Rosengren, Hjalmar
Published: (2024)

Construction of constitutive relationships for simple in Noll’s sense materials with viscoelastic-viscoplastic behavior
by: Lepikhin, P.P.
Published: (2009)

Electronic proofs and economic court
by: A. M. Naichenko
Published: (2017)

Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations
by: Bouarroudj, Sofiane, et al.
Published: (2020)

On virial expansions of correlation functions. Canonical ensemble
by: Yu. Pohorielov, et al.
Published: (2023)

Solutions of the Kirkwood–Salsburg equation for a lattice classical system of one-dimensional oscillators with positive finite-range many-body interaction potentials
by: Skrypnik, W. I., et al.
Published: (2008)

New Combinatorial Formulae for Nested Bethe Vectors
by: Kosmakov, Maksim, et al.
Published: (2025)

Mathematical description of the charged particles system near the surface of the porous membrane
by: Gorunovich, V. V., et al.
Published: (1987)

Property of mixing of continuous classical systems with strong superstable interactions
by: Rebenko, A. L., et al.
Published: (2017)

Object of burden of proof in civil proceedings
by: N. B. Fartushok
Published: (2015)

Another proof for the continuity of the Lipsman mapping
by: A. Messaoud, et al.
Published: (2020)

The proof-structure of the transcendental deduction of categories
by: Yu. Fedorchenko
Published: (2015)

Another proof for the continuity of the Lipsman mapping
by: Messaoud, A., et al.
Published: (2020)

Formula for multiplication of solutions of the Cortevegs—de Fries equations
by: Fushchich , V. I., et al.
Published: (1992)

Peterson’s algorithm Total correctness proof in IPCL
by: Zhygallo, A.A.
Published: (2018)

Legal nature of electronic proofs in the economic court
by: A. M. Naichenko
Published: (2017)

Peterson’s Algorithm total correctness proof in IPCL
by: Zhygallo, A.A.
Published: (2016)

Local Proof of Algebraic Characterization of Free Actions
by: Baum, P.F., et al.
Published: (2014)

Erratum to the paper F.S. Rofe-Beketov "Operator-Theoretical Proof of the Arnold Alternation Theorem and its Generalization"
Published: (2013)

On Simple-Layer Potentials for One Class of Pseudodifferential Equations
by: M. M. Osypchuk, et al.
Published: (2015)

On Simple-Layer Potentials for One Class of Pseudodifferential Equations
by: Osipchuk, M. M., et al.
Published: (2015)

Distribution of eigenvalues and trace formula for the Sturm–Liouville operator equation
by: Aslanova, N. M., et al.
Published: (2010)