youngkit is an offline, exact-integer command-line toolkit for integer partitions, Young diagrams and Young tableaux. It is intended for students and researchers in combinatorics, and for anyone who wants to calculate an exact count or apply a standard bijection without writing a program. It uses Go's standard library and makes no network calls.
Build the command from the repository root with Go:
go build -o youngkit .This creates the youngkit executable in the current directory.
The command has twelve subcommands. Their usage forms are:
youngkit count N [--max-part K] [--distinct]
youngkit list N [--max-part K] [--limit L]
youngkit rank SHAPE
youngkit unrank N RANK
youngkit conjugate SHAPE
youngkit hooks SHAPE [--entries K]
youngkit compare A B
youngkit neighbors SHAPE
youngkit rsk ENTRY... | youngkit rsk -
youngkit unrsk P Q
youngkit syt SHAPE [--index K] [--limit L]
youngkit core K SHAPE
For rsk, provide permutation entries as arguments, or use - as the sole argument to read whitespace-separated entries from standard input. Options are written after the command's positional arguments and may also be interspersed with them.
A shape is written as comma-separated, positive, nonincreasing parts, for example 5,3,3,1. The notation 0 denotes the empty shape. Parts must be canonical integers: malformed notation such as a leading-zero part (03), a trailing comma, or an empty shape string is rejected.
A run of equal parts may be written PARTxCOUNT with the lowercase letter x: 4,3x2,1 is 4,3,3,1, 2x3 is 2,2,2 and 3x1 is 3. PART and COUNT are canonical integers, COUNT runs from 1 to 5000, and the total size limit is unchanged. Every command that takes a shape accepts the run notation and prints the parts spelled out; 0 stays the only spelling of the empty shape, so 0x1 is rejected as a zero part.
A tableau is written with slash-separated rows and comma-separated entries, for example 1,3,5/2,4/6; 0 denotes the empty tableau. Standard tableaux contain each integer from 1 through the tableau's size exactly once, with entries increasing from left to right in every row and from top to bottom in every column. Empty rows, malformed entries and tableaux that fail these conditions are rejected.
Counts and ranks are exact integers. Shape and tableau commands accept 0 for their empty object; its printed form is also 0.
count counts partitions of a nonnegative integer, optionally limiting the largest part and requiring distinct parts.
list prints the first partitions in reverse lexicographic order, with an optional largest-part bound and result limit.
rank reports a shape's zero-based position among the partitions of its size and the total number of such partitions.
unrank returns the shape at a zero-based partition position, using an exact integer rank.
conjugate reflects a shape across its diagonal and prints its Ferrers diagram.
hooks prints every cell's hook length and the exact standard-tableau count; --entries also requests the semistandard-tableau count for that entry bound.
compare compares two equal-size shapes by dominance and reports their partial sums.
neighbors lists the shapes formed by adding or removing one box.
rsk applies Robinson–Schensted to a permutation and reports its insertion and recording tableaux, along with its longest increasing and decreasing subsequence lengths.
unrsk validates two standard tableaux of the same shape and recovers their permutation by inverse Robinson–Schensted.
syt counts and lists standard Young tableaux in the documented order; --index jumps to a position and --limit bounds the number shown.
core computes a shape's k-core, weight and runner quotient shapes using the abacus.
Examples:
youngkit hooks 4,3,1 --entries 3 exits with 0 and prints:
shape 4,3,1
size 8
hook 6 4 3 1
hook 4 2 1
hook 1
syt 70
entries 3
ssyt 15
youngkit rsk 2 5 1 4 3 exits with 0 and prints:
perm 2 5 1 4 3
shape 2,2,1
lis 2
lds 3
p 1 3
p 2 4
p 5
q 1 2
q 3 4
q 5
youngkit core 3 5,4,1 exits with 0 and prints:
shape 5,4,1
k 3
core 2,1,1
weight 2
quotient 0=0
quotient 1=1
quotient 2=1
A successful command exits with status 0. A command or input error exits with status 2, writes one youngkit: -prefixed diagnostic followed by LF to standard error, and writes nothing to standard output. Successful output lines end with LF.
main.go- The executable entry point passes process arguments and standard streams to the CLI.internal/base- Shared input, option, integer, text and error primitives live here.internal/shape- Shape parsing, diagrams, dominance and Young's lattice operations live here.internal/count- Partition generation, ranking and exact hook-based counts live here.internal/tableau- Tableau operations, Robinson–Schensted and abacus calculations live here.internal/cli- The twelve commands and their dispatch live here.
Run these checks from the repository root:
gofmt -l .
go vet ./...
go test ./...The project uses only the Go standard library, so these checks require no external service or runtime dependency.
MIT, see LICENSE.
Built with BAKED