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Problem results

ProblemsClear skill: Exponential Generating Functions Build a practice set

COMB:9931264Mathematical problem title

Exponential Generating FunctionsFactorial NormalizationLabeled ProductLabel AllocationEnumerative Combinatorics Problem Solving

Exponential generating functions and labeled structuresEnumerative Combinatorics · Calculation

COMB:9931265Mathematical problem title

Exponential Generating FunctionsEgf DerivativePointingDistinguished Extra LabelEnumerative Combinatorics Problem Solving

Exponential generating functions and labeled structuresEnumerative Combinatorics · Calculation

COMB:9931266Mathematical problem title

Exponential Generating FunctionsExponential FormulaUnordered ComponentsFree Block OrderingEnumerative Combinatorics Problem Solving

Exponential generating functions and labeled structuresEnumerative Combinatorics · Mixed review

COMB:9931267Mathematical problem title

Exponential Generating FunctionsStirling EgfBell Bivariate SeriesBlock Count MarkerEnumerative Combinatorics Problem Solving

Exponential generating functions and labeled structuresEnumerative Combinatorics · Calculation

COMB:9931268Mathematical problem title

Exponential Generating FunctionsSingleton Free PartitionsExponential RestrictionDistinguished Block RecurrenceEnumerative Combinatorics Problem Solving

Exponential generating functions and labeled structuresEnumerative Combinatorics · Calculation

COMB:9931269Mathematical problem title

Exponential Generating FunctionsPairs And TriplesRestricted Block SeriesFactorial Profile CountEnumerative Combinatorics Problem Solving

Exponential generating functions and labeled structuresEnumerative Combinatorics · Calculation

COMB:9931270Mathematical problem title

Exponential Generating FunctionsSurjection EgfNamed FibresOccupancy RestrictionsEnumerative Combinatorics Problem Solving

Exponential generating functions and labeled structuresEnumerative Combinatorics · Calculation

COMB:9931271Mathematical problem title

Exponential Generating FunctionsDerangement EgfForbidden Singleton CyclesAlternating RecurrenceEnumerative Combinatorics Problem Solving

Exponential generating functions and labeled structuresEnumerative Combinatorics · Calculation

COMB:9931272Mathematical problem title

Exponential Generating FunctionsInvolution Bivariate EgfFixed Point MarkerMarked Label AverageEnumerative Combinatorics Problem Solving

Exponential generating functions and labeled structuresEnumerative Combinatorics · Mixed review

COMB:9931273Mathematical problem title

Exponential Generating FunctionsOdd Cycle PermutationsCycle Size RestrictionDifferential RecurrenceEnumerative Combinatorics Problem Solving

Exponential generating functions and labeled structuresEnumerative Combinatorics · Mixed review

COMB:9931274Mathematical problem title

Exponential Generating FunctionsConnected Labeled GraphsLogarithm OF AssembliesDistinguished ComponentEnumerative Combinatorics Problem Solving

Exponential generating functions and labeled structuresEnumerative Combinatorics · Mixed review

COMB:9931275Mathematical problem title

Exponential Generating FunctionsUnordered Set OF ListsLah NumbersInternal Block OrderEnumerative Combinatorics Problem Solving

Exponential generating functions and labeled structuresEnumerative Combinatorics · Calculation

COMB:9931276Mathematical problem title

Exponential Generating FunctionsOrdered Set PartitionsSequence OF BlocksFirst Block RecurrenceEnumerative Combinatorics Problem Solving

Exponential generating functions and labeled structuresEnumerative Combinatorics · Calculation

COMB:9931277Mathematical problem title

Exponential Generating FunctionsMarked ComponentsFactorial MomentsAverage Block CountEnumerative Combinatorics Problem Solving

Exponential generating functions and labeled structuresEnumerative Combinatorics · Mixed review

COMB:9931278Mathematical problem title

Exponential Generating FunctionsIncreasing Binary TreesEgf Differential EquationMinimum Root BijectionEnumerative Combinatorics Problem Solving

Exponential generating functions and labeled structuresEnumerative Combinatorics · Mixed review

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COMB:9931264Mathematical problem title

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COMB:9931267Mathematical problem title

COMB:9931268Mathematical problem title

COMB:9931269Mathematical problem title

COMB:9931270Mathematical problem title

COMB:9931271Mathematical problem title

COMB:9931272Mathematical problem title

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COMB:9931274Mathematical problem title

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COMB:9931276Mathematical problem title

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COMB:9931278Mathematical problem title

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COMB:9931264If $a_n$ counts structures on a specified set of n distinct labels, its exponential generating function is A(x)=\sum_…Mathematical problem title

COMB:9931265For $A(x)=\sum$ $a_nx^n/n$ !, interpret A'(x) as structures on n ordinary labels together with one fixed extra label $\star$ .Mathematical problem title

COMB:9931266Let $b_j$ count allowed component structures on a specified j-element label set, with $b_0=0$ , and let B(x)=\sum_{j\ge1…Mathematical problem title

COMB:9931267Let S(n,k) count partitions of an n-element labeled set into k nonempty blocks.Mathematical problem title

COMB:9931268Let $a_n$ count set partitions of [n] with no singleton blocks, including $a_0=1$ .Mathematical problem title

COMB:9931269Let $a_n$ count set partitions of [n] in which every block has size two or three.Mathematical problem title

COMB:9931270For fixed $k\ge$ 1, let $s_{n,k}$ count surjections from [n] to the named target set [k].Mathematical problem title

COMB:9931271Let $D_n$ count permutations of [n] with no fixed points, with $D_0=1$ .Mathematical problem title

COMB:9931272Let $I_n(u)$ be the polynomial that sums u^{f(\pi )} over involutions $\pi$ of [n], where $f(\pi$ ) is the number of fixe…Mathematical problem title

COMB:9931273Let $a_n$ count permutations of [n] whose disjoint cycles all have odd length.Mathematical problem title

COMB:9931274Let $g_n$ count simple undirected graphs on the labeled vertex set [n], and let $c_n$ count connected ones for $n\ge$ 1.Mathematical problem title

COMB:9931275Partition an n-element labeled set into k nonempty blocks, put a linear order on the labels inside each block, and…Mathematical problem title

COMB:9931276An ordered set partition is a sequence of nonempty disjoint blocks whose union is the full label set; the labels wi…Mathematical problem title

COMB:9931277Suppose assemblies of nonempty labeled components have bivariate EGF $A(x,u)=\exp(uH(x))$ , where u marks the number o…Mathematical problem title

COMB:9931278Consider rooted binary trees on the distinct labels [n], with designated left and right child positions, either of…Mathematical problem title

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