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arxiv: 2509.25446 · v3 · submitted 2025-09-29 · 🧮 math.CO

On the combinatorics of tableaux -- A notebook of open problems

Dale R. Worley This is my paper

Pith reviewed 2026-05-18 11:57 UTC · model grok-4.3

classification 🧮 math.CO
keywords Young tableauxcombinatoricsopen problemsunsolved problemsKourovka Notebooktableaux enumerationcombinatorial identities
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The pith

This notebook collects unsolved problems in the combinatorics of tableaux and invites contributions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper assembles a list of open questions in the combinatorics of tableaux, patterned directly on the Kourovka Notebook of group theory problems. It presents these questions as a living document to which the research community is encouraged to add new problems or report solutions. A sympathetic reader would see value in concentrating scattered open questions into one place so that progress in tableaux theory can be tracked and accelerated over time. The format treats the notebook itself as the main contribution rather than any single theorem.

Core claim

The author has compiled a set of unsolved problems concerning tableaux and related combinatorial structures, modeled after established problem notebooks in other areas of mathematics, and explicitly invites readers to submit additions or resolutions to keep the collection current and useful.

What carries the argument

The notebook format that organizes and describes individual open problems in Young tableaux and related objects without attempting to solve them.

If this is right

  • Each listed problem, once solved, supplies a concrete advance in the enumeration or structural understanding of tableaux.
  • Community contributions can expand the collection with newly identified questions.
  • The notebook serves as a centralized reference that researchers can consult to avoid duplicating work on already-solved questions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same notebook style could be applied to other subfields of combinatorics that lack a dedicated problem list.
  • Regular updates would turn the notebook into an ongoing map of the frontiers in tableaux research.
  • Cross-references between problems might reveal unexpected connections that individual papers overlook.

Load-bearing premise

The problems listed are accurately described as open and have not been resolved in the existing literature.

What would settle it

A published solution appearing in the literature that solves one of the listed problems without citing this notebook would demonstrate that the problem was not open at the time the notebook was compiled.

read the original abstract

Inspired by the the Kourovka Notebook of unsolved problems in group theory [KhukhMaz2024], this is a notebook of unsolved problems in the combinatorics of tableaux. Contributions to the notebook are invited.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 1 minor

Summary. The manuscript compiles a collection of open problems in the combinatorics of tableaux, presented in the style of the Kourovka Notebook of unsolved problems in group theory. It lists specific questions on Young tableaux and related objects without asserting new theorems or proofs, and explicitly invites community contributions to solve or expand the list.

Significance. If the problems are correctly identified as open, the notebook could serve as a useful reference for directing research in tableaux combinatorics, analogous to established problem collections in other mathematical fields. Its value would lie in centralizing questions to stimulate progress and collaboration rather than in any single result.

minor comments (1)
  1. [Abstract] Abstract: the phrase 'Inspired by the the Kourovka Notebook' contains a duplicated word and should be corrected to 'Inspired by the Kourovka Notebook'.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their review and for recommending minor revision. We are pleased that the manuscript is viewed as a potentially useful centralized collection of open problems in tableaux combinatorics, modeled after the Kourovka Notebook, with value in stimulating community contributions rather than presenting new theorems.

Circularity Check

0 steps flagged

No circularity: compilation of open problems with no derivations or predictions

full rationale

The paper is explicitly a Kourovka-style notebook collecting unsolved problems in tableaux combinatorics and inviting contributions. It contains no theorems, derivations, equations, predictions, fitted parameters, or self-referential claims. The sole framing—that the listed questions are currently open—is a factual assertion about the external literature rather than an internal logical step that could reduce to its own inputs. No load-bearing argument exists that could be circular by construction, self-citation, or renaming.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a problem list rather than a theoretical paper, so no free parameters, axioms, or invented entities support a central claim.

pith-pipeline@v0.9.0 · 5538 in / 839 out tokens · 39073 ms · 2026-05-18T11:57:52.323176+00:00 · methodology

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