LRCALC(1)

📦 version 1.2, in debian bookworm, debian trixie, ubuntu jammy, ubuntu noble, ubuntu questing, ubuntu resolute, ubuntu stonking

💖 lrcalc(1) — the user manual, but make it a group chat 💖

okay bestie so this is the manual page for lrcalc, section 1 of the User Manuals, and I need you to lock in because Littlewood-Richardson coefficients are literally the moment. it's a command-line calculator for symmetric function stuff and it ATE. no cap. 🎀

✨ NAME ✨

lrcalc — Calculate with Littlewood-Richardson coefficients 💅

🌈 SYNOPSIS 🌈

lrcalc coprod [-a] part
lrcalc lrcoef outer - inner1 - inner2
lrcalc lrtab [-r rows] outer / inner
lrcalc mult [-mz] [-r rows] [-q rows,cols] [-f rows,level] part1 - part2
lrcalc skew [-m] [-r rows] outer / inner

🦋 coprod — Calculate coproducts in the ring of symmetric functions 🦋

DESCRIPTION

the command lrcalc coprod z lists every single pair of partitions x and y where the Littlewood-Richardson coefficient c^z_{x,y} is non-zero, and it puts that coefficient right up front. it's giving "here's the tea, and here's how many times it happens." ✨

OPTIONS

  • -a — not documented 🙈 (yeah, we don't know either, bestie. it's mysterious. main character energy.)

EXAMPLE

% lrcalc coprod 3 2 1
1  (3, 1)  (2)
1  (2, 2)  (1, 1)
1  (3, 1)  (1, 1)
1  (2, 1)  (3)
2  (2, 1)  (2, 1)
1  (2, 2, 1)  (1)
1  (3, 2, 1)  ()
1  (3, 2)  (1)
1  (2, 1, 1)  (2)
1  (3, 1, 1)  (1)
1  (1, 1, 1)  (2, 1)
1  (2, 1, 1)  (1, 1)
1  (2, 2)  (2)

see that lonely 2 in the middle? iconic. she's the only one not doing a solo. 💀

💜 lrcoef — Compute a single Littlewood-Richardson coefficient 💜

DESCRIPTION

the command lrcalc lrcoef z - x - y computes the Littlewood-Richardson coefficient c^z_{x,y}, which is literally the coefficient of the Schur function s_z in the product s_x * s_y. one number. no list. just vibes and one coefficient. periodt. 👑

EXAMPLE

% lrcalc lrcoef 3 2 1 - 2 1 - 2 1
2

slay. 💅

🌸 lrtab 🌸

not documented 🫶

(i know. i know. she's mysterious. she's not telling us anything. respect her privacy. ✨)

🔥 mult — Expand a product of two Schur functions in the basis of Schur functions 🔥

DESCRIPTION

the command lrcalc mult x - y lists every partition z where the Littlewood-Richardson coefficient c^z_{x,y} is non-zero, with that coefficient sitting right in front. it's the full guest list and how many plus-ones each one brought. 🎀

OPTIONS

  • -mz — not documented 🙈
  • -r rows — not documented 🙈
  • -q rows,cols — Calculates quantum coefficients. Experimental feature. ⚠️ (so like, it works, but she's still in her testing era, yk?)
  • -f rows,level — Calculates fusion coefficients. Experimental feature. ⚠️ (same energy. experimental. handle with care, bestie.)

EXAMPLES

% lrcalc mult 2 1 - 2 1
1  (3, 3)
1  (4, 2)
1  (2, 2, 1, 1)
1  (2, 2, 2)
2  (3, 2, 1)
1  (4, 1, 1)
1  (3, 1, 1, 1)
% lrcalc mult -f 3,2 3 2 1 - 3 2 1
1  (4, 4, 4)
1  (5, 4, 3)
% lrcalc mult -q 3,2 3 2 1 - 3 2 1
1  (2)
1  (1, 1)

look at the fusion one and the quantum one side by side, they're giving completely different aesthetics and honestly? both serve. 🦋

⭐ skew — Expand a skew Schur function in the basis of Schur functions ⭐

DESCRIPTION

the command lrcalc skew z / x lists all partitions y for which the Littlewood-Richardson coefficient c^z_{x,y} is non-zero, with that coefficient in front. she's the slashed one. the diva. the / girlie. 💅

OPTIONS

  • -m — not documented 🙈
  • -r rows — not documented 🙈

EXAMPLE

% lrcalc skew 3 2 1 / 2 1
1  (3)
2  (2, 1)
1  (1, 1, 1)

okay (2, 1) showed up twice and honestly? deserved. 👑

🫶 AUTHOR 🫶

Anders S. Buch <asbuch at math rutgers edu>

🧚 MANPAGE AUTHOR 🧚

Tobias Hansen <thansen at debian dot org>

and that's the whole page, bestie!! 🌈 this one's from Linux, dated AUGUST 2013, and it's the LRCALC(1) page of the User Manuals — so go forth, run lrcalc, and make those Littlewood-Richardson coefficients feel seen. mwah. 💖🎀🦋🌸✨

📦 where this page comes from