Pith Number

pith:XMBITKOJ

pith:2026:XMBITKOJX2BDPYPCW2PRMRZOTI

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On Tournament Anti-Sidorenko Orientations of Trees

Felix Christian Clemen, Hao Chen, Jonathan A. Noel

Oriented paths with exactly one non-leaf source or sink are tournament anti-Sidorenko.

arxiv:2605.14138 v1 · 2026-05-13 · math.CO

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Claims

C1strongest claim

Every oriented path with at least three arcs and exactly one non-leaf source or sink vertex is tournament anti-Sidorenko. An oriented path is tournament anti-Sidorenko if the distance between any leaf vertex and any source or sink vertex is at least two and the distance between any pair of non-leaf source or sink vertices is a multiple of four. Every spider with exactly three legs admits a tournament anti-Sidorenko orientation.

C2weakest assumption

The proofs for the stated distance conditions and structural properties of the oriented paths and spiders hold without gaps or unstated restrictions on the graphs considered.

C3one line summary

Specific orientations of paths with distance conditions and three-legged spiders are tournament anti-Sidorenko, proving conjectures and yielding new families.

References

30 extracted · 30 resolved · 0 Pith anchors

[1] A. Basit, B. Granet, D. Horsley, A. K¨ undgen, and K. Staden. The semi-inducibility problem. E-print arXiv:2501.09842v2, 2025 2025

[2] N. Behague, G. Crudele, J. A. Noel, and L. M. Simbaqueba. Sidorenko-Type Inequalities for Pairs of Trees.Random Structures Algorithms, 67(1):Paper No. e70026, 2025 2025

[3] N. Behague, N. Morrison, and J. A. Noel. Off-diagonal commonality of graphs via entropy.SIAM J. Discrete Math., 38(3):2335–2360, 2024 2024

[4] V. Bitonti, E. Hogan, J. A. Noel, and D. Tsarev. Relative Sidorenko inequalities in oriented graphs. In preparation, 2026 2026

[5] G. Blekherman and A. Raymond. A path forward: tropicalization in extremal combi- natorics.Adv. Math., 407:Paper No. 108561, 68, 2022 2022

Receipt and verification

First computed	2026-05-17T23:39:11.720455Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb0289a9c9be8237e1e2b69f16472e9a2e4f4e7bbe50ffd6ed243b3d8a477632

Aliases

arxiv: 2605.14138 · arxiv_version: 2605.14138v1 · doi: 10.48550/arxiv.2605.14138

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/XMBITKOJX2BDPYPCW2PRMRZOTI \
  | 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: bb0289a9c9be8237e1e2b69f16472e9a2e4f4e7bbe50ffd6ed243b3d8a477632

Canonical record JSON

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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-13T21:44:25Z",
    "title_canon_sha256": "c978ff09e75bccabbfd738469fedfd8afbf2fa17bf1ccc7d5dec1d729f2e7e09"
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