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Named Identities

Alphabetical index to identities
	A	B	C	D	E	F	G	H	I
	J	K	L	M	N	O	P	Pascal	Q
	R	S	T	U	V	W	X	Y	Z

Abel's Identities
Cat: # 3900048

some early examples


Absorption
Cat: #2400002
      
      


Alternating Row Identity
Cat: # 3610001



Basic Additive Identity
Cat: # 1100001


Basic Multiplicative Identity
Cat: # 2400001


Binomial Harmonic Identity
Cat: # 3900004


Binomial Theorem
Cat: # 3900000


Binomial Theorem for falling factorial
Cat: # 3900022


Brinkman's Identity
Cat: # 3500009



Catalan numbers
Cat: # 2500002


Cauchy's Formula
Cat: # 3700001


The Christmas Stocking Theorem
Cat: # 1100002



The Derangement Formulas
Cat: # 3900006


Dixon's Identity
Cat: # 3610003




Factorial fractional representation
Cat: # 2300001


Falling factorial representation
Cat: # 2300002


Fibonacci binomial representation
Catalog #: 1200003




The Hexagon property (a.k.a. The Star of David rule)
Catalog #: 2100002


The Hockey Stick Theorem
Catalog #: 3400001



The Inversion Formula
Catalog #: 3700005




k-binomial representation
Catalog #: 1200015


Kruskal-Katona Theorem
Catalog #: 1200016

numbers based on the k-binomial representation of m = |A|


Lucas' Theorem
Catalog #: 5100007
are the base p representations of n and k



Orthogonality
Cat: # 3610006

 
Generalized Orthogonality
Cat: # 3610007




Partial row sum rule
Cat: # 1100005



Pascal's 1^st Identity
Cat: # 1100001


Pascal's 2^nd Identity
Cat: # 1100002


Pascal's 3^rd Identity
Cat: # 1100003


Pascal's 4^th Identity
Cat: # 1000001


Pascal's 5^th Identity (parts 1 and 2)
Cat: # 1100004

Cat: # 1200001


Pascal's 6^th Identity
Cat: # 1100005


Pascal's 7^th Identity
Cat: # 2400001


Pascal's 8^th Identity
Cat: #2400002
      
      


Pascal's 9^th Identity
Cat: # 1500001


Pascal's 10^th Identity
Cat: # 1500002


Pascal's 11^th Identity
Cat: # 1100006


Pascal's 12^th Identity
Cat: # 2400003


Pascal's Last Identity
Cat: # 2300003




Reed-Dawson Identity
Cat: # 3500008


Row Sum Identity
Cat: # 1200001



Sperner's Theorem
Cat: # 1200014

where F is a set of subsets of the set {1, 2, ..., n} such that no element of F is a subset of another element of F (this type of set sometimes called an antichain)

The Star of David rule (a.k.a. The Hexagon property)
Catalog #: 2100002


The Star of David g.c.d. rule
Catalog #: 5300001


Summations (Upper and Parallel, respectively)
Cat: # 1100002


Symmetry
Cat: # 1000001



Trinomial Revision
Cat: # 2100001



Upper Negation
Cat: # 2400004



Vandermonde's Convolution
Cat: # 3100003

Special case: m = 0


Worpitzky's Identity
Cat: # 3900001
where is from Euler's Triangle