18.212 Algebraic Combinatorics Notes
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18.212 Algebraic Combinatorics Notes
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Zettelkasten
Math
Algebra
inverse permutation
involution
Category Theory
partially ordered set (poset)
Theoretical CS
increasing binary tree
Unfiled
absorption probability
adjacency matrix of product of graphs is tensor of adjacency matrices
arborescence
BEST theorem
Cauchy-Binet formula
complement of a graph
complete bipartite graph
complete graph
cone over a graph
Cramer's rule
directed matrix tree theorem
effective resistance
electrical network
Eulerian cycle
f_G (graph)
f_G of disjoint union
hypercube graph
incidence matrix
increasing tree
Kirchoff's laws
Kirchoff's matrix of an electrical network
Kirchoff's matrix tree theorem
labelled tree
Laplacian (Kirchoff) matrix
Linstrom-Gessel-Viennot theorem
number of labellings on a tree with given degrees
number of parking functions
oriented incidence matrix of a graph is totally unimodal
oriented incidence matrix
parking function
paths on differential posets and rooks
potential function
product of graphs
reciprocity formula for f_G
reduced Laplacian matrix
regular graph
simple graph
small degree polys don't intersect hyperplanes everywhere
spanning tree
spectrum of a graph
totally unimodal matrix
walks on differential posets
weighted matrix tree theorem
Y-delta transform
18.212 Algebraic Combinatorics
Abel's binomial formula
adjacency matrix
antichain
associated poset to a permutation
bijection between size k subsets and n-k subsets
Boolean lattice
Catalan numbers
Cayley's formula
chain
conjugate partition
covering relation
cycles of a permutation
DeBruijn's theorem
descent of a permutation
differential poset
Dilworth's theorem
distinct parts and partitions with less than k parts
Dyck path
Dyck paths is Catalan
equidistributed
Euler's pentagonal number theorem
Eulerian numbers are coefficients of Eulerian polynomial
Eulerian numbers
Eulerian polynomial
Eulerian statistic
Eulerian triangle
exceedance is equidistributed to antiexceedance
exceedance is Eulerian
exceedance
Ferrers shape
Fibonacci's lattice
first entry of schensted shape is length of longest increasing subsequence
generalized binomial theorem
generating function for size of young diagrams
generating function
Greene's theorem (posets)
Greene's theorem
Hardy-Ramanujan's theorem
Hasse diagram
hook length formula
hook length
inversion of a permutation
Jacobi's triple product formula
k-queue sortable
Knuth's hook length formula for trees
lambda(P(w)) is schensted shape
lambda(poset)
lattice of order ideals
Mahonian statistic
Major index
Mirsky's theorem
multiplicity of a partition
Narayana numbers
Narayana triangle
necessary conditions for scd
number of 3-permutation-avoiding permutations is catalan
number of complete binary trees with n+1 leaves is catalan
number of increasing binary trees with n vertices and k left edges is Eulerian numbers
number of non-cross perfect matchings with 2n vertices is catalan
number of non-crossing partitions with n vertices is catalan
number of permutations that are 2-queue sortable is catalan
number of permutations that are stack-sortable is catalan
number of plane binary trees with n vertices is Catalan
number of triangulations of a convex (n+2)-gon is catalan
number of valid parenthesization of n+1 letters is catalan
partition function
partition
partitions with odd parts is equal to partitions with distinct parts
pattern avoidance
pentagonal numbers
permutation
plane binary tree
product of chains has a SCD
product of posets
q-analog
q-binomial coefficient
q-binomial coefficients are generating functions for size of bounded young diagrams
q-factorial is generating functions of inversions of permutations
q-factorial
q-number
rank numbers
rank symmetric poset
rank unimodal poset
ranked poset
record (permutation)
records is Sterlingian
Robinson-Schensted-Knud (RSK) correspondence
saturated chain
Schensted insertion algorithm
Schensted shape
Sperner poset
Sperner's theorem
stack-sortable
statistic on permutations
Sterlingian statistic
sum over squares of number of SYTs is n!
symmetric chain decomposition
the number of SYTs of shape (n, n) is catalan
valid parenthesizations
weak exceedance
Young diagram
Young tableau(x)
Young's lattice
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Abel's binomial formula
Tags:
#theorem
Statement
(
x
+
y
)
n
=
∑
k
=
0
n
(
n
k
)
y
(
y
+
k
z
)
k
−
1
(
x
−
k
z
)
n
−
k
Proof