A Bijective Proof of Stanley's Shuffling Theorem

1985 ◽  
Vol 288 (1) ◽  
pp. 147
Author(s):  
I. P. Goulden
Keyword(s):  
Bijective Proof

A bijective proof of a q-analogue of the sum of cubes using overpartitions

2017 ◽  
Vol 10 (3) ◽  
pp. 523-530
Author(s):  
Jacob Forster ◽  
Kristina Garrett ◽  
Luke Jacobsen ◽  
Adam Wood
Keyword(s):  
Bijective Proof

scholarly journals A direct bijective proof of the hook-length formula

1997 ◽  
Vol Vol. 1 ◽  
Author(s):  
Jean-Christophe Novelli ◽  
Igor Pak ◽  
Alexander V. Stoyanovskii
Keyword(s):  
Young Tableaux ◽  
Hook Length ◽  
Bijective Proof ◽  
International Audience ◽  
Standard Young Tableaux

International audience This paper presents a new proof of the hook-length formula, which computes the number of standard Young tableaux of a given shape. After recalling the basic definitions, we present two inverse algorithms giving the desired bijection. The next part of the paper presents the proof of the bijectivity of our construction. The paper concludes with some examples.

scholarly journals On the Distribution of Depths in Increasing Trees

10.37236/409 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Markus Kuba ◽  
Stephan Wagner
Keyword(s):  
Common Ancestor ◽  
Short Note ◽  
Bijective Proof ◽  
Lowest Common Ancestor ◽  
Recursive Trees

By a theorem of Dobrow and Smythe, the depth of the $k$th node in very simple families of increasing trees (which includes, among others, binary increasing trees, recursive trees and plane ordered recursive trees) follows the same distribution as the number of edges of the form $j-(j+1)$ with $j < k$. In this short note, we present a simple bijective proof of this fact, which also shows that the result actually holds within a wider class of increasing trees. We also discuss some related results that follow from the bijection as well as a possible generalization. Finally, we use another similar bijection to determine the distribution of the depth of the lowest common ancestor of two nodes.

scholarly journals A bijective proof of Riordan's theorem on powers of Fibonacci numbers

1999 ◽  
Vol 199 (1-3) ◽  
pp. 217-220
Author(s):  
Andrej Dujella
Keyword(s):  
Fibonacci Numbers ◽  
Bijective Proof

scholarly journals A Bijective Proof for a Theorem of Ehrhart

2009 ◽  
Vol 116 (8) ◽  
pp. 688-701 ◽  
Author(s):  
Steven V Sam
Keyword(s):  
Bijective Proof

scholarly journals A bijective proof of Amdeberhan’s conjecture on the number of(s,s+2)-core partitions with distinct parts

2018 ◽  
Vol 341 (5) ◽  
pp. 1294-1300 ◽  
Author(s):  
Jineon Baek ◽  
Hayan Nam ◽  
Myungjun Yu
Keyword(s):  
Bijective Proof
Sign in / Sign up

Export Citation Format

Share Document