An Elementary Proof of Stirling's Formula

1986 ◽  
Vol 93 (2) ◽  
pp. 123-125 ◽  
Author(s):  
P. Diaconis ◽  
D. Freedman
Keyword(s):  
Elementary Proof ◽  
Stirling’S Formula

scholarly journals An Elementary Proof of Bevan's Theorem on the Growth of Grid Classes of Permutations

2019 ◽  
Vol 62 (4) ◽  
pp. 975-984
Author(s):  
Michael Albert ◽  
Vincent Vatter
Keyword(s):  
Growth Rate ◽  
Singular Value Decomposition ◽  
Hadamard Product ◽  
Elementary Proof ◽  
Singular Value ◽  
Stirling’S Formula ◽  
Real Numbers ◽  
Singular Vectors ◽  
Value Decomposition ◽  
Method Of Lagrange Multipliers

AbstractBevan established that the growth rate of a monotone grid class of permutations is equal to the square of the spectral radius of a related bipartite graph. We give an elementary and self-contained proof of a generalization of this result using only Stirling's formula, the method of Lagrange multipliers, and the singular value decomposition of matrices. Our proof relies on showing that the maximum over the space of n × n matrices with non-negative entries summing to one of a certain function of those entries, parametrized by the entries of another matrix Γ of non-negative real numbers, is equal to the square of the largest singular value of Γ and that the maximizing point can be expressed as a Hadamard product of Γ with the tensor product of singular vectors for its greatest singular value.

An Elementary Proof of Stirling's Formula

1986 ◽  
Vol 93 (2) ◽  
pp. 123 ◽  
Author(s):  
P. Diaconis ◽  
D. Freedman
Keyword(s):  
Elementary Proof ◽  
Stirling’S Formula

A New Elementary Proof of Stirling's Formula

1995 ◽  
Vol 68 (1) ◽  
pp. 55 ◽  
Author(s):  
C. L. Frenzen
Keyword(s):  
Elementary Proof ◽  
Stirling’S Formula

scholarly journals On Stirling’s formula

2021 ◽  
Vol 47 ◽  
Author(s):  
Juozas J. Mačys
Keyword(s):  
Relative Error ◽  
Elementary Proof ◽  
Stirling’S Formula

Approaches to the proof of Stirling’s formula are compared. Elementary proof of very exact variant of formula (with relative error 1/(1260n5)) is given.

AN ELEMENTARY PROOF OF A THEOREM OF LEE

1991 ◽  
Vol 11 (3) ◽  
pp. 356-360 ◽  
Author(s):  
Jia'an Yan
Keyword(s):  
Elementary Proof

scholarly journals A new elementary proof of a theorem of Minkowski

1926 ◽  
Vol 2 (3) ◽  
pp. 97-99
Author(s):  
Matsusaburô Fujiwara
Keyword(s):  
Elementary Proof

scholarly journals Antisymmetry of the Stochastical Order on all Ordered Topological Spaces

2019 ◽  
Vol 7 (1) ◽  
pp. 250-252 ◽  
Author(s):  
Tobias Fritz
Keyword(s):  
Topological Space ◽  
General Result ◽  
Elementary Proof ◽  
Short Note ◽  
Stochastic Order ◽  
Topological Spaces ◽  
Probability Measures ◽  
Ordered Topological Space ◽  
Special Cases

Abstract In this short note, we prove that the stochastic order of Radon probability measures on any ordered topological space is antisymmetric. This has been known before in various special cases. We give a simple and elementary proof of the general result.

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