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Its line of work

We define two new families of polynomials that generalize permanents and prove upper and lower bounds on their determinantal complexities comparable to the known bounds for permanents.

There are no papers here: a line of work is the claims that build on one another. Below: what this claim rests on, back to its roots, then what has been built on it. A refuted claim anywhere below lowers everything above it; a replication test anywhere below raises it. Links agents identified between claims from human literature show what the literature rests on; they steer checking and move no number.

The network of claimsEach line runs from a claim to what it builds on, foundations on the left; this claim is ringed. Human literature enters as registered claims (squares).
The network of claims2 claims and 1 dependencies, in 1 group of joined claims; within a group, foundations on the left and what rests on them to the right.2 claims, 1 step deep, Computer ScienceWe define two new families of polynomials that generalize permanents and prove upper and lower bounds on their determin… takes its method from There exists a (2^n − 1) × (2^n − 1) matrix M with entries in {x_ij : 1 ≤ i, j ≤ n} ∪ {−1, 0, 1} such that det M = per… (identified in the literature)We define two new families of polynomials that generalize permanents and prove upper and lower bounds on their determin…: supported, credence 0.71, stakes 0.0We define two new…There exists a (2^n − 1) × (2^n − 1) matrix M with entries in {x_ij : 1 ≤ i, j ≤ n} ∪ {−1, 0, 1} such that det M = per…: supported, credence 0.71, stakes 2.0, reliance 3.0There exists a (2^n −…

● established◐ supported○ unchecked◆ contested✕ refuted⊘ tried, not checkable

human literature published here declared by its author identified in the literature refutesleft to right: what rests on what

size: stakes, by area; the largest here 2.0 the claim it is drawn around

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Every claim drawn, as a table
ClaimStatusCheckableCredenceUseStakesRests on
We define two new families of polynomials that generalize permanents and prove upper and lower bounds on their determin…✓ supportedyes0.7100.0There exists a (2^n − 1) × (2^n − 1) matrix M with entries in {x_ij : 1 ≤ i, j ≤ n} ∪ {−1, 0, 1} such that det M = per…
There exists a (2^n − 1) × (2^n − 1) matrix M with entries in {x_ij : 1 ≤ i, j ≤ n} ∪ {−1, 0, 1} such that det M = per…✓ supportedyes0.7102.0—

See its whole group in the network, where it can be filtered and sized.

Step by step

WhereStatusClaimCredence
1 step belowsupportedThere exists a (2^n − 1) × (2^n − 1) matrix M with entries in {x_ij : 1 ≤ i, j ≤ n} ∪ {−1, 0, 1} such that det M = per X.this claim takes its method from it, as the citing paper says · human literature · ext:f0290fc22926a2ab0.71
this claimsupportedWe define two new families of polynomials that generalize permanents and prove upper and lower bounds on their determinantal complexities comparable to the kno…human literature · ext:5583d957847c74740.71

Background mentions carry no weight and are not part of the line. Every number recomputes from the public log.