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Combinatorics, statistics, and FindStat

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(1)

Combinatorics, statistics, and FindStat

Viviane Pons, Universit¨at Wien

UC Davis

November 13, 2013

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(2)

Combinatorial objects and bijections

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(3)

Combinatorial objects and bijections

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(4)

Combinatorial objects and bijections

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(5)

Combinatorial statistics

Area = 6 Height = 3 Right subtree = 3

Height = 3 Leaves = 5 No right subtree = 5 Touch points = 3 Internal nodes = 3 Left branch = 3

Initial rise = 2 Root subtrees = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(6)

Combinatorial statistics

Area = 6

Height = 3 Right subtree = 3 Height = 3 Leaves = 5 No right subtree = 5 Touch points = 3 Internal nodes = 3 Left branch = 3

Initial rise = 2 Root subtrees = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(7)

Combinatorial statistics

Area = 6

Height = 3 Right subtree = 3

Height = 3

Leaves = 5 No right subtree = 5 Touch points = 3 Internal nodes = 3 Left branch = 3

Initial rise = 2 Root subtrees = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(8)

Combinatorial statistics

Area = 6

Height = 3 Right subtree = 3

Height = 3

Leaves = 5 No right subtree = 5

Touch points = 3

Internal nodes = 3 Left branch = 3 Initial rise = 2 Root subtrees = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(9)

Combinatorial statistics

Area = 6

Height = 3 Right subtree = 3

Height = 3

Leaves = 5 No right subtree = 5

Touch points = 3

Internal nodes = 3 Left branch = 3

Initial rise = 2

Root subtrees = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(10)

Combinatorial statistics

Area = 6 Height = 3

Right subtree = 3

Height = 3

Leaves = 5 No right subtree = 5

Touch points = 3

Internal nodes = 3 Left branch = 3

Initial rise = 2

Root subtrees = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(11)

Combinatorial statistics

Area = 6 Height = 3

Right subtree = 3

Height = 3 Leaves = 5

No right subtree = 5

Touch points = 3

Internal nodes = 3 Left branch = 3

Initial rise = 2

Root subtrees = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(12)

Combinatorial statistics

Area = 6 Height = 3

Right subtree = 3

Height = 3 Leaves = 5

No right subtree = 5

Touch points = 3 Internal nodes = 3

Left branch = 3

Initial rise = 2

Root subtrees = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(13)

Combinatorial statistics

Area = 6 Height = 3

Right subtree = 3

Height = 3 Leaves = 5

No right subtree = 5

Touch points = 3 Internal nodes = 3

Left branch = 3

Initial rise = 2 Root subtrees = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(14)

Combinatorial statistics

Area = 6 Height = 3 Right subtree = 3

Height = 3 Leaves = 5

No right subtree = 5

Touch points = 3 Internal nodes = 3

Left branch = 3

Initial rise = 2 Root subtrees = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(15)

Combinatorial statistics

Area = 6 Height = 3 Right subtree = 3

Height = 3 Leaves = 5 No right subtree = 5 Touch points = 3 Internal nodes = 3

Left branch = 3

Initial rise = 2 Root subtrees = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(16)

Combinatorial statistics

Area = 6 Height = 3 Right subtree = 3

Height = 3 Leaves = 5 No right subtree = 5 Touch points = 3 Internal nodes = 3 Left branch = 3

Initial rise = 2 Root subtrees = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(17)

Combinatorial statistics

Area = 6 Height = 3 Right subtree = 3

Height = 3 Leaves = 5 No right subtree = 5 Touch points = 3 Internal nodes = 3 Left branch = 3

Initial rise = 2 Root subtrees = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(18)

Combinatorial statistics

Area = 6 Height = 3 Right subtree = 3

Height = 3 Leaves = 5 No right subtree = 5 Touch points = 3 Internal nodes = 3 Left branch = 3

Initial rise = 2 Root subtrees = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(19)

Touch points 3 2 1 2 1

Height 1 2 2 2 3

Root subtrees 3 2 1 2 1

Height 1 2 2 2 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(20)

Touch points = 3 Root subtrees = 3

Height = 3 Height = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(21)

Touch points = 3 Root subtrees = 3

Height = 3 Height = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(22)

Touch points = 3 Root subtrees = 3

Height = 3 Height = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(23)

Touch points = 3 Root subtrees = 3

Height = 3 Height = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(24)

Touch points = 3 Root subtrees = 3

Height = 3 Height = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(25)

Touch points = 3 Root subtrees = 3

Height = 3 Height = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(26)

Touch points = 3 Root subtrees = 3

Height = 3 Height = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(27)

Touch points = 3 Root subtrees = 3

Height = 3 Height = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(28)

Touch points = 3 Root subtrees = 3

Height = 3 Height = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

(29)

Touch points = 3 Root subtrees = 3

Height = 3 Height = 3

Viviane Pons, Universit¨at Wien Combinatorics, statistics, and FindStat

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