Return to Answer

I'm going to interpret this as a request for examples of results that were announced a while ago but whose proofs have not yet appeared. In other words, people don't doubt that the result is correct and that the author(s) can prove it, and there is an expectation that the current lack of a proof will not be a permanent state of affairs (i.e., a paper with the proof will be written and made public eventually).

One example of this is Rota's Conjecture on excluded minor characterizations of matroids representable over a given finite field. This was announced in 2014 by Geelen, Gerards, and Whittle, but apart from the sketch in that Notices article, no further details have yet appeared.

EDIT: An example of a paper that cites this unpublished work, and relies on it in an essential way, is The matroid secretary problem for minor-closed classes and random matroids by Tony Huynh and Peter Nelson. After stating Theorem 2, Huynh and Nelson write:

To be forthright with the reader, we stress that Theorem 2 relies on a structural hypothesis communicated to us by Geelen, Gerards, and Whittle, which has not yet appeared in print. This hypothesis is stated as Hypothesis 1. The proof of Hypothesis 1 will stretch to hundreds of pages, and will be a consequence of their decade-plus ‘matroid minors project’. This is a body of work generalising Robertson and Seymour’s graph minors structure theorem to matroids representable over a fixed finite field, leading to a solution of Rota’s Conjecture.

Another example is On the existence of asymptotically good linear codes in minor-closed classes by Peter Nelson and Stefan H. M. van Zwam, IEEE Trans. Info. Theory 61 (2015), 1153–1158. The results of Nelson and van Zwamm have in turn been used in an essential way to prove Theorem 1.4 of Girth conditions and Rota's basis conjecture by Benjamin Friedman and Sean McGuinness.

I'm going to interpret this as a request for examples of results that were announced a while ago but whose proofs have not yet appeared. In other words, people don't doubt that the result is correct and that the author(s) can prove it, and there is an expectation that the current lack of a proof will not be a permanent state of affairs (i.e., a paper with the proof will be written and made public eventually).

One example of this is Rota's Conjecture on excluded minor characterizations of matroids representable over a given finite field. This was announced in 2014 by Geelen, Gerards, and Whittle, but apart from the sketch in that Notices article, no further details have yet appeared.

EDIT: An example of a paper that cites this unpublished work, and relies on it in an essential way, is The matroid secretary problem for minor-closed classes and random matroids by Tony Huynh and Peter Nelson. After stating Theorem 2, Huynh and Nelson write:

To be forthright with the reader, we stress that Theorem 2 relies on a structural hypothesis communicated to us by Geelen, Gerards, and Whittle, which has not yet appeared in print. This hypothesis is stated as Hypothesis 1. The proof of Hypothesis 1 will stretch to hundreds of pages, and will be a consequence of their decade-plus ‘matroid minors project’. This is a body of work generalising Robertson and Seymour’s graph minors structure theorem to matroids representable over a fixed finite field, leading to a solution of Rota’s Conjecture.

Another example is On the existence of asymptotically good linear codes in minor-closed classes by Peter Nelson and Stefan H. M. van Zwam, IEEE Trans. Info. Theory 61 (2015), 1153–1158. The results of Nelson and van Zwamm have in turn been used in an essential way to prove Theorem 1.4 of Girth conditions and Rota's basis conjecture by Benjamin Friedman and Sean McGuinness.

I'm going to interpret this as a request for examples of results that were announced a while ago but whose proofs have not yet appeared. In other words, people don't doubt that the result is correct and that the author(s) can prove it, and there is an expectation that the current lack of a proof will not be a permanent state of affairs (i.e., a paper with the proof will be written and made public eventually).

One example of this is Rota's Conjecture on excluded minor characterizations of matroids representable over a given finite field. This was announced in 2014 by Geelen, Gerards, and Whittle, but apart from the sketch in that Notices article, no further details have yet appeared.

EDIT: An example of a paper that cites this unpublished work, and relies on it in an essential way, is The matroid secretary problem for minor-closed classes and random matroids by Tony Huynh and Peter Nelson. After stating Theorem 2, Huynh and Nelson write:

To be forthright with the reader, we stress that Theorem 2 relies on a structural hypothesis communicated to us by Geelen, Gerards, and Whittle, which has not yet appeared in print. This hypothesis is stated as Hypothesis 1. The proof of Hypothesis 1 will stretch to hundreds of pages, and will be a consequence of their decade-plus ‘matroid minors project’. This is a body of work generalising Robertson and Seymour’s graph minors structure theorem to matroids representable over a fixed finite field, leading to a solution of Rota’s Conjecture.

I'm going to interpret this as a request for examples of results that were announced a while ago but whose proofs have not yet appeared. In other words, people don't doubt that the result is correct and that the author(s) can prove it, and there is an expectation that the current lack of a proof will not be a permanent state of affairs (i.e., a paper with the proof will be written and made public eventually).

One example of this is Rota's Conjecture on excluded minor characterizations of matroids representable over a given finite field. This was announced in 2014 by Geelen, Gerards, and Whittle, but apart from the sketch in that Notices article, no further details have yet appeared.

EDIT: An example of a paper that cites this unpublished work, and relies on it in an essential way, is The matroid secretary problem for minor-closed classes and random matroids by Tony Huynh and Peter Nelson. After stating Theorem 2, Huynh and Nelson write:

To be forthright with the reader, we stress that Theorem 2 relies on a structural hypothesis communicated to us by Geelen, Gerards, and Whittle, which has not yet appeared in print. This hypothesis is stated as Hypothesis 1. The proof of Hypothesis 1 will stretch to hundreds of pages, and will be a consequence of their decade-plus ‘matroid minors project’. This is a body of work generalising Robertson and Seymour’s graph minors structure theorem to matroids representable over a fixed finite field, leading to a solution of Rota’s Conjecture.

Another example is On the existence of asymptotically good linear codes in minor-closed classes by Peter Nelson and Stefan H. M. van Zwam, IEEE Trans. Info. Theory 61 (2015), 1153–1158. The results of Nelson and van Zwamm have in turn been used in an essential way to prove Theorem 1.4 of Girth conditions and Rota's basis conjecture by Benjamin Friedman and Sean McGuinness.

I'm going to interpret this as a request for examples of results that were announced a while ago but whose proofs have not yet appeared. In other words, people don't doubt that the result is correct and that the author(s) can prove it, and there is an expectation that the current lack of a proof will not be a permanent state of affairs (i.e., a paper with the proof will be written and made public eventually). For example, the papers by Arthur mentioned by Buzzard seem to fall into this category.

One example of this is Rota's Conjecture on excluded minor characterizations of matroids representable over a given finite field. This was announced in 2014 by Geelen, Gerards, and Whittle, but apart from the sketch in that Notices article, no further details have yet appeared.

EDIT: An example of a paper that cites this unpublished work, and relies on it in an essential way, is The matroid secretary problem for minor-closed classes and random matroids by Tony Huynh and Peter Nelson. After stating Theorem 2, Huynh and Nelson write:

To be forthright with the reader, we stress that Theorem 2 relies on a structural hypothesis communicated to us by Geelen, Gerards, and Whittle, which has not yet appeared in print. This hypothesis is stated as Hypothesis 1. The proof of Hypothesis 1 will stretch to hundreds of pages, and will be a consequence of their decade-plus ‘matroid minors project’. This is a body of work generalising Robertson and Seymour’s graph minors structure theorem to matroids representable over a fixed finite field, leading to a solution of Rota’s Conjecture.

I'm going to interpret this as a request for examples of results that were announced a while ago but whose proofs have not yet appeared. In other words, people don't doubt that the result is correct and that the author(s) can prove it, and there is an expectation that the current lack of a proof will not be a permanent state of affairs (i.e., a paper with the proof will be written and made public eventually).

One example of this is Rota's Conjecture on excluded minor characterizations of matroids representable over a given finite field. This was announced in 2014 by Geelen, Gerards, and Whittle, but apart from the sketch in that Notices article, no further details have yet appeared.

EDIT: An example of a paper that cites this unpublished work, and relies on it in an essential way, is The matroid secretary problem for minor-closed classes and random matroids by Tony Huynh and Peter Nelson. After stating Theorem 2, Huynh and Nelson write:

To be forthright with the reader, we stress that Theorem 2 relies on a structural hypothesis communicated to us by Geelen, Gerards, and Whittle, which has not yet appeared in print. This hypothesis is stated as Hypothesis 1. The proof of Hypothesis 1 will stretch to hundreds of pages, and will be a consequence of their decade-plus ‘matroid minors project’. This is a body of work generalising Robertson and Seymour’s graph minors structure theorem to matroids representable over a fixed finite field, leading to a solution of Rota’s Conjecture.