Learn · Combinatorics
Axeyum for combinatorialists
Axeyum combines a constructive finite-carrier library with proof-producing search and certificate-producing symbolic computation.
a103b3db3 Measured Source Axeyum fact ledger and implementation documentation After reading this guide, you should be able to
Learning objectives
- Identify the parts of Axeyum that are relevant to combinatorics.
- Distinguish implemented results from the current research frontier.
- Open a lesson or artifact that provides the underlying definitions and evidence.
Current state
How do proof, search, and symbolic computation meet in finite mathematics?
The kernel library includes finite sets, multisets, permutations, binomial coefficients, inclusion-exclusion, and pigeonhole principles. Separate SAT searches establish optimal sorting-network results and finite Rado-number results. The computer algebra system proves binomial sums and recurrence identities by creative telescoping.
These routes expose different kinds of evidence. Kernel terms support general theorems, SAT certificates settle bounded searches, and computer algebra certificates verify exact recurrences and sums.
Why it matters
What the current work makes possible
- One site shows deductive, exhaustive-search, and symbolic certificates for related finite problems.
- The finite carriers beneath the results are constructive and reusable.
- The ledger distinguishes established general theorems from bounded computational results.
- Two finite Rado results are recorded as locally novel rather than as formalizations of known theorems.
Results to inspect
Open the evidence
What comes next
Extend the present base
The formal library can next add graphs, matchings, paths, extremal principles, and a general generating-function development.
The solver route can extend certified bounded results while the kernel route extracts reusable lemmas from successful searches.
Where to begin