- FindStat

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Identifier

St000198: Binary trees ⟶ ℤ

Values

. => 0

[.,.] => 2

[.,[.,.]] => 10

[[.,.],.] => 12

[.,[.,[.,.]]] => 42

[.,[[.,.],.]] => 44

[[.,.],[.,.]] => 50

[[.,[.,.]],.] => 52

[[[.,.],.],.] => 56

[.,[.,[.,[.,.]]]] => 170

[.,[.,[[.,.],.]]] => 172

[.,[[.,.],[.,.]]] => 178

[.,[[.,[.,.]],.]] => 180

[.,[[[.,.],.],.]] => 184

[[.,.],[.,[.,.]]] => 202

[[.,.],[[.,.],.]] => 204

[[.,[.,.]],[.,.]] => 210

[[[.,.],.],[.,.]] => 226

[[.,[.,[.,.]]],.] => 212

[[.,[[.,.],.]],.] => 216

[[[.,.],[.,.]],.] => 228

[[[.,[.,.]],.],.] => 232

[[[[.,.],.],.],.] => 240

[.,[.,[.,[.,[.,.]]]]] => 682

[.,[.,[.,[[.,.],.]]]] => 684

[.,[.,[[.,.],[.,.]]]] => 690

[.,[.,[[.,[.,.]],.]]] => 692

[.,[.,[[[.,.],.],.]]] => 696

[.,[[.,.],[.,[.,.]]]] => 714

[.,[[.,.],[[.,.],.]]] => 716

[.,[[.,[.,.]],[.,.]]] => 722

[.,[[[.,.],.],[.,.]]] => 738

[.,[[.,[.,[.,.]]],.]] => 724

[.,[[.,[[.,.],.]],.]] => 728

[.,[[[.,.],[.,.]],.]] => 740

[.,[[[.,[.,.]],.],.]] => 744

[.,[[[[.,.],.],.],.]] => 752

[[.,.],[.,[.,[.,.]]]] => 810

[[.,.],[.,[[.,.],.]]] => 812

[[.,.],[[.,.],[.,.]]] => 818

[[.,.],[[.,[.,.]],.]] => 820

[[.,.],[[[.,.],.],.]] => 824

[[.,[.,.]],[.,[.,.]]] => 842

[[.,[.,.]],[[.,.],.]] => 844

[[[.,.],.],[.,[.,.]]] => 906

[[[.,.],.],[[.,.],.]] => 908

[[.,[.,[.,.]]],[.,.]] => 850

[[.,[[.,.],.]],[.,.]] => 866

[[[.,.],[.,.]],[.,.]] => 914

[[[.,[.,.]],.],[.,.]] => 930

[[[[.,.],.],.],[.,.]] => 962

[[.,[.,[.,[.,.]]]],.] => 852

[[.,[.,[[.,.],.]]],.] => 856

[[.,[[.,.],[.,.]]],.] => 868

[[.,[[.,[.,.]],.]],.] => 872

[[.,[[[.,.],.],.]],.] => 880

[[[.,.],[.,[.,.]]],.] => 916

[[[.,.],[[.,.],.]],.] => 920

[[[.,[.,.]],[.,.]],.] => 932

[[[[.,.],.],[.,.]],.] => 964

[[[.,[.,[.,.]]],.],.] => 936

[[[.,[[.,.],.]],.],.] => 944

[[[[.,.],[.,.]],.],.] => 968

[[[[.,[.,.]],.],.],.] => 976

[[[[[.,.],.],.],.],.] => 992

[.,[.,[.,[.,[.,[.,.]]]]]] => 2730

[.,[.,[.,[.,[[.,.],.]]]]] => 2732

[.,[.,[.,[[.,.],[.,.]]]]] => 2738

[.,[.,[.,[[.,[.,.]],.]]]] => 2740

[.,[.,[.,[[[.,.],.],.]]]] => 2744

[.,[.,[[.,.],[.,[.,.]]]]] => 2762

[.,[.,[[.,.],[[.,.],.]]]] => 2764

[.,[.,[[.,[.,.]],[.,.]]]] => 2770

[.,[.,[[[.,.],.],[.,.]]]] => 2786

[.,[.,[[.,[.,[.,.]]],.]]] => 2772

[.,[.,[[.,[[.,.],.]],.]]] => 2776

[.,[.,[[[.,.],[.,.]],.]]] => 2788

[.,[.,[[[.,[.,.]],.],.]]] => 2792

[.,[.,[[[[.,.],.],.],.]]] => 2800

[.,[[.,.],[.,[.,[.,.]]]]] => 2858

[.,[[.,.],[.,[[.,.],.]]]] => 2860

[.,[[.,.],[[.,.],[.,.]]]] => 2866

[.,[[.,.],[[.,[.,.]],.]]] => 2868

[.,[[.,.],[[[.,.],.],.]]] => 2872

[.,[[.,[.,.]],[.,[.,.]]]] => 2890

[.,[[.,[.,.]],[[.,.],.]]] => 2892

[.,[[[.,.],.],[.,[.,.]]]] => 2954

[.,[[[.,.],.],[[.,.],.]]] => 2956

[.,[[.,[.,[.,.]]],[.,.]]] => 2898

[.,[[.,[[.,.],.]],[.,.]]] => 2914

[.,[[[.,.],[.,.]],[.,.]]] => 2962

[.,[[[.,[.,.]],.],[.,.]]] => 2978

[.,[[[[.,.],.],.],[.,.]]] => 3010

[.,[[.,[.,[.,[.,.]]]],.]] => 2900

[.,[[.,[.,[[.,.],.]]],.]] => 2904

[.,[[.,[[.,.],[.,.]]],.]] => 2916

[.,[[.,[[.,[.,.]],.]],.]] => 2920

[.,[[.,[[[.,.],.],.]],.]] => 2928

[.,[[[.,.],[.,[.,.]]],.]] => 2964

[.,[[[.,.],[[.,.],.]],.]] => 2968

[.,[[[.,[.,.]],[.,.]],.]] => 2980

>>> Load all 626 entries. <<<

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

$F_{1} = q^{2}$

$F_{2} = q^{10} + q^{12}$

$F_{3} = q^{42} + q^{44} + q^{50} + q^{52} + q^{56}$

$F_{4} = q^{170} + q^{172} + q^{178} + q^{180} + q^{184} + q^{202} + q^{204} + q^{210} + q^{212} + q^{216} + q^{226} + q^{228} + q^{232} + q^{240}$

$F_{5} = q^{682} + q^{684} + q^{690} + q^{692} + q^{696} + q^{714} + q^{716} + q^{722} + q^{724} + q^{728} + q^{738} + q^{740} + q^{744} + q^{752} + q^{810} + q^{812} + q^{818} + q^{820} + q^{824} + q^{842} + q^{844} + q^{850} + q^{852} + q^{856} + q^{866} + q^{868} + q^{872} + q^{880} + q^{906} + q^{908} + q^{914} + q^{916} + q^{920} + q^{930} + q^{932} + q^{936} + q^{944} + q^{962} + q^{964} + q^{968} + q^{976} + q^{992}$

$F_{6} = q^{2730} + q^{2732} + q^{2738} + q^{2740} + q^{2744} + q^{2762} + q^{2764} + q^{2770} + q^{2772} + q^{2776} + q^{2786} + q^{2788} + q^{2792} + q^{2800} + q^{2858} + q^{2860} + q^{2866} + q^{2868} + q^{2872} + q^{2890} + q^{2892} + q^{2898} + q^{2900} + q^{2904} + q^{2914} + q^{2916} + q^{2920} + q^{2928} + q^{2954} + q^{2956} + q^{2962} + q^{2964} + q^{2968} + q^{2978} + q^{2980} + q^{2984} + q^{2992} + q^{3010} + q^{3012} + q^{3016} + q^{3024} + q^{3040} + q^{3242} + q^{3244} + q^{3250} + q^{3252} + q^{3256} + q^{3274} + q^{3276} + q^{3282} + q^{3284} + q^{3288} + q^{3298} + q^{3300} + q^{3304} + q^{3312} + q^{3370} + q^{3372} + q^{3378} + q^{3380} + q^{3384} + q^{3402} + q^{3404} + q^{3410} + q^{3412} + q^{3416} + q^{3426} + q^{3428} + q^{3432} + q^{3440} + q^{3466} + q^{3468} + q^{3474} + q^{3476} + q^{3480} + q^{3490} + q^{3492} + q^{3496} + q^{3504} + q^{3522} + q^{3524} + q^{3528} + q^{3536} + q^{3552} + q^{3626} + q^{3628} + q^{3634} + q^{3636} + q^{3640} + q^{3658} + q^{3660} + q^{3666} + q^{3668} + q^{3672} + q^{3682} + q^{3684} + q^{3688} + q^{3696} + q^{3722} + q^{3724} + q^{3730} + q^{3732} + q^{3736} + q^{3746} + q^{3748} + q^{3752} + q^{3760} + q^{3778} + q^{3780} + q^{3784} + q^{3792} + q^{3808} + q^{3850} + q^{3852} + q^{3858} + q^{3860} + q^{3864} + q^{3874} + q^{3876} + q^{3880} + q^{3888} + q^{3906} + q^{3908} + q^{3912} + q^{3920} + q^{3936} + q^{3970} + q^{3972} + q^{3976} + q^{3984} + q^{4000} + q^{4032}$

$F_{7} = q^{10922} + q^{10924} + q^{10930} + q^{10932} + q^{10936} + q^{10954} + q^{10956} + q^{10962} + q^{10964} + q^{10968} + q^{10978} + q^{10980} + q^{10984} + q^{10992} + q^{11050} + q^{11052} + q^{11058} + q^{11060} + q^{11064} + q^{11082} + q^{11084} + q^{11090} + q^{11092} + q^{11096} + q^{11106} + q^{11108} + q^{11112} + q^{11120} + q^{11146} + q^{11148} + q^{11154} + q^{11156} + q^{11160} + q^{11170} + q^{11172} + q^{11176} + q^{11184} + q^{11202} + q^{11204} + q^{11208} + q^{11216} + q^{11232} + q^{11434} + q^{11436} + q^{11442} + q^{11444} + q^{11448} + q^{11466} + q^{11468} + q^{11474} + q^{11476} + q^{11480} + q^{11490} + q^{11492} + q^{11496} + q^{11504} + q^{11562} + q^{11564} + q^{11570} + q^{11572} + q^{11576} + q^{11594} + q^{11596} + q^{11602} + q^{11604} + q^{11608} + q^{11618} + q^{11620} + q^{11624} + q^{11632} + q^{11658} + q^{11660} + q^{11666} + q^{11668} + q^{11672} + q^{11682} + q^{11684} + q^{11688} + q^{11696} + q^{11714} + q^{11716} + q^{11720} + q^{11728} + q^{11744} + q^{11818} + q^{11820} + q^{11826} + q^{11828} + q^{11832} + q^{11850} + q^{11852} + q^{11858} + q^{11860} + q^{11864} + q^{11874} + q^{11876} + q^{11880} + q^{11888} + q^{11914} + q^{11916} + q^{11922} + q^{11924} + q^{11928} + q^{11938} + q^{11940} + q^{11944} + q^{11952} + q^{11970} + q^{11972} + q^{11976} + q^{11984} + q^{12000} + q^{12042} + q^{12044} + q^{12050} + q^{12052} + q^{12056} + q^{12066} + q^{12068} + q^{12072} + q^{12080} + q^{12098} + q^{12100} + q^{12104} + q^{12112} + q^{12128} + q^{12162} + q^{12164} + q^{12168} + q^{12176} + q^{12192} + q^{12224} + q^{12970} + q^{12972} + q^{12978} + q^{12980} + q^{12984} + q^{13002} + q^{13004} + q^{13010} + q^{13012} + q^{13016} + q^{13026} + q^{13028} + q^{13032} + q^{13040} + q^{13098} + q^{13100} + q^{13106} + q^{13108} + q^{13112} + q^{13130} + q^{13132} + q^{13138} + q^{13140} + q^{13144} + q^{13154} + q^{13156} + q^{13160} + q^{13168} + q^{13194} + q^{13196} + q^{13202} + q^{13204} + q^{13208} + q^{13218} + q^{13220} + q^{13224} + q^{13232} + q^{13250} + q^{13252} + q^{13256} + q^{13264} + q^{13280} + q^{13482} + q^{13484} + q^{13490} + q^{13492} + q^{13496} + q^{13514} + q^{13516} + q^{13522} + q^{13524} + q^{13528} + q^{13538} + q^{13540} + q^{13544} + q^{13552} + q^{13610} + q^{13612} + q^{13618} + q^{13620} + q^{13624} + q^{13642} + q^{13644} + q^{13650} + q^{13652} + q^{13656} + q^{13666} + q^{13668} + q^{13672} + q^{13680} + q^{13706} + q^{13708} + q^{13714} + q^{13716} + q^{13720} + q^{13730} + q^{13732} + q^{13736} + q^{13744} + q^{13762} + q^{13764} + q^{13768} + q^{13776} + q^{13792} + q^{13866} + q^{13868} + q^{13874} + q^{13876} + q^{13880} + q^{13898} + q^{13900} + q^{13906} + q^{13908} + q^{13912} + q^{13922} + q^{13924} + q^{13928} + q^{13936} + q^{13962} + q^{13964} + q^{13970} + q^{13972} + q^{13976} + q^{13986} + q^{13988} + q^{13992} + q^{14000} + q^{14018} + q^{14020} + q^{14024} + q^{14032} + q^{14048} + q^{14090} + q^{14092} + q^{14098} + q^{14100} + q^{14104} + q^{14114} + q^{14116} + q^{14120} + q^{14128} + q^{14146} + q^{14148} + q^{14152} + q^{14160} + q^{14176} + q^{14210} + q^{14212} + q^{14216} + q^{14224} + q^{14240} + q^{14272} + q^{14506} + q^{14508} + q^{14514} + q^{14516} + q^{14520} + q^{14538} + q^{14540} + q^{14546} + q^{14548} + q^{14552} + q^{14562} + q^{14564} + q^{14568} + q^{14576} + q^{14634} + q^{14636} + q^{14642} + q^{14644} + q^{14648} + q^{14666} + q^{14668} + q^{14674} + q^{14676} + q^{14680} + q^{14690} + q^{14692} + q^{14696} + q^{14704} + q^{14730} + q^{14732} + q^{14738} + q^{14740} + q^{14744} + q^{14754} + q^{14756} + q^{14760} + q^{14768} + q^{14786} + q^{14788} + q^{14792} + q^{14800} + q^{14816} + q^{14890} + q^{14892} + q^{14898} + q^{14900} + q^{14904} + q^{14922} + q^{14924} + q^{14930} + q^{14932} + q^{14936} + q^{14946} + q^{14948} + q^{14952} + q^{14960} + q^{14986} + q^{14988} + q^{14994} + q^{14996} + q^{15000} + q^{15010} + q^{15012} + q^{15016} + q^{15024} + q^{15042} + q^{15044} + q^{15048} + q^{15056} + q^{15072} + q^{15114} + q^{15116} + q^{15122} + q^{15124} + q^{15128} + q^{15138} + q^{15140} + q^{15144} + q^{15152} + q^{15170} + q^{15172} + q^{15176} + q^{15184} + q^{15200} + q^{15234} + q^{15236} + q^{15240} + q^{15248} + q^{15264} + q^{15296} + q^{15402} + q^{15404} + q^{15410} + q^{15412} + q^{15416} + q^{15434} + q^{15436} + q^{15442} + q^{15444} + q^{15448} + q^{15458} + q^{15460} + q^{15464} + q^{15472} + q^{15498} + q^{15500} + q^{15506} + q^{15508} + q^{15512} + q^{15522} + q^{15524} + q^{15528} + q^{15536} + q^{15554} + q^{15556} + q^{15560} + q^{15568} + q^{15584} + q^{15626} + q^{15628} + q^{15634} + q^{15636} + q^{15640} + q^{15650} + q^{15652} + q^{15656} + q^{15664} + q^{15682} + q^{15684} + q^{15688} + q^{15696} + q^{15712} + q^{15746} + q^{15748} + q^{15752} + q^{15760} + q^{15776} + q^{15808} + q^{15882} + q^{15884} + q^{15890} + q^{15892} + q^{15896} + q^{15906} + q^{15908} + q^{15912} + q^{15920} + q^{15938} + q^{15940} + q^{15944} + q^{15952} + q^{15968} + q^{16002} + q^{16004} + q^{16008} + q^{16016} + q^{16032} + q^{16064} + q^{16130} + q^{16132} + q^{16136} + q^{16144} + q^{16160} + q^{16192} + q^{16256}$

Description

A decimal representation of a binary tree as a code word.
Code word constructed by mapping a binary tree to its corresponding set of matching parentheses and then replacing every ( with a $1$ and every ) with a $0$. We then convert the resulting binary code word to a decimal number.

Code

def treeToParenthesis(t):
    singletonTree = BinaryTree(None)  
    parenthesisRepresentation = '()'
    if (t ==singletonTree):
        return None
    else:
        if (t[0] == singletonTree and t[1] == singletonTree):
            return parenthesisRepresentation
        if (t[0] != singletonTree):
            parenthesisRepresentation='('+treeToParenthesis(t[0])+')'
        if (t[1] != singletonTree):
            parenthesisRepresentation+= treeToParenthesis(t[1])
        return parenthesisRepresentation

def treeToDecimal(t):
    parenthesisRepresentation = treeToParenthesis(t)
    decimalRepresentation = 0
    if parenthesisRepresentation == None:
        return decimalRepresentation
    length = len(parenthesisRepresentation)
    for x in range(1,length+1):
        if parenthesisRepresentation[length-x] == "(":
            decimalRepresentation += 2**(x-1)
    return decimalRepresentation

def statistic(t):
    return treeToDecimal(t)

Created

May 16, 2014 at 02:50 by Kyle Ryan

Updated

Dec 30, 2016 at 10:59 by Christian Stump