Pith Number

pith:BO5WLVDD

pith:2026:BO5WLVDDNN3M22AZVE2AIJOU3J

not attested not anchored not stored refs resolved

Note on a magic rectangle set on dihedral group

Sylwia Cichacz

Magic rectangle sets exist for every dihedral group of order mnk when m and n are even.

arxiv:2605.13393 v1 · 2026-05-13 · math.CO

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\pithnumber{BO5WLVDDNN3M22AZVE2AIJOU3J}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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Claims

C1strongest claim

We prove that MRS_Γ(m,n;k) exists for every dihedral group Γ of order mnk, provided that m and n are even. As a consequence, we obtain broad existence results for magic rectangles and magic squares over dihedral groups.

C2weakest assumption

The construction requires m and n even so that elements can be paired and ordered to produce constant products despite the non-commutative relations in the dihedral group.

C3one line summary

Magic rectangle sets exist over dihedral groups of order mnk whenever m and n are even.

References

11 extracted · 11 resolved · 0 Pith anchors

[1] Cichacz, Partition of Abelian groups into zero-sum sets by complete mappings and its application to the existence of a magic rectangle set,J 2025

[2] S. Cichacz, D. Froncek, Magic squares on Abelian groups,Discrete Math. 349(7)(2026), 115033 2026

[3] S. Cichacz, D. Froncek, Semi-magic dihedral squares, Preprint arXiv:2602.20774 [math.CO] (2026) 2026

[4] S. Cichacz, T. Hinc, A magic rectangle set on Abelian groups and its application,Discrete Appl. Math.288(2021), 201–210. 10 2021

[5] C. J. Colbourn, J. H. Dinitz, eds.,Handbook of combinatorial designs, second edn.,Discrete Mathematics and its Applications (Boca Raton), Chapman & Hill/CRC Press, Boca Raton, FL 2007 2007

Receipt and verification

First computed	2026-05-18T02:44:47.691454Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0bbb65d4636b76cd6819a9340425d4da7973ae26d38e9ffe1b83c839ecd0bdb5

Aliases

arxiv: 2605.13393 · arxiv_version: 2605.13393v1 · doi: 10.48550/arxiv.2605.13393 · pith_short_12: BO5WLVDDNN3M · pith_short_16: BO5WLVDDNN3M22AZ · pith_short_8: BO5WLVDD

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BO5WLVDDNN3M22AZVE2AIJOU3J \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0bbb65d4636b76cd6819a9340425d4da7973ae26d38e9ffe1b83c839ecd0bdb5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8fcca7da7d8f3969e08e34d3c4646daec9ed7f2c3f3573a8b241a82289efd7c0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-13T11:51:05Z",
    "title_canon_sha256": "1a6c2bb849a18c64563c1f7f94b538e066692eedacac3694f18db8410f874283"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13393",
    "kind": "arxiv",
    "version": 1
  }
}