Skip to content

Record four 2026 lower bounds for the Shannon capacity of C₇ - #174

Open
Chessing234 wants to merge 1 commit into
teorth:mainfrom
Chessing234:update/c9-shannon-2026
Open

Record four 2026 lower bounds for the Shannon capacity of C₇#174
Chessing234 wants to merge 1 commit into
teorth:mainfrom
Chessing234:update/c9-shannon-2026

Conversation

@Chessing234

Copy link
Copy Markdown
Contributor

Refs #168 (item 2).

The C₉ page still stopped at Polak–Schrijver $367^{1/5}\approx 3.2578$ (2018). Four later constructions, all checked against the arXiv texts rather than a summary:

  • Itty–Rosin–Carstensen–Reichman, arXiv:2607.21517: independent set of size $134753$ in $C_7^{\boxtimes 10}$, so $\Theta(C_7)\ge 134753^{1/10}\approx 3.258020$.
  • Gao, arXiv:2607.27869: recursive product giving $\Theta(C_7)\ge 3.258789153908\ldots$ from an independent set in $C_7^{\boxtimes 200}$.
  • Buys–Polak–Zuiddam, arXiv:2607.29681: $\Theta(C_7)\ge 3.258805369885\ldots$, Lean-formalized.
  • Tandon, arXiv:2608.30273: heterogeneous recursion, $\Theta(C_7)\ge 3.25883262\ldots$ from an independent set in $C_7^{\boxtimes 500}$.

The README cell is updated to the last of these, the bound table keeps the history in chronological order, and the other odd-cycle bounds from BPZ are noted on the page rather than split into new constants.

Construction/certificate links from the papers are in the comments column. AI was used to locate the papers; every numerical claim above was read from the source.

Test plan

  • Recomputed $134753^{1/10}$ and $367^{1/5}$ locally
  • Checked each bound against the arXiv abstract/theorem statement
  • README table cell matches the last lower-bound row
  • No open PR already covering C₉

Made with Cursor

The page still listed Polak–Schrijver 367^{1/5} ≈ 3.2578 after four later constructions (Itty–Rosin–Carstensen–Reichman, Gao, Buys–Polak–Zuiddam, Tandon).
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment

Labels

None yet

Projects

None yet

Development

Successfully merging this pull request may close these issues.

1 participant