Rota's excluded minors conjecture is one of a number of conjectures made by the mathematician Gian-Carlo Rota. It is considered an important problem by...

and matroid theory, Rota's basis conjecture is an unproven conjecture concerning rearrangements of bases, named after Gian-Carlo Rota. It states that, if...

Massachusetts. Kallman–Rota inequality Rota's conjecture Rota's basis conjecture Rota–Baxter algebra Joint spectral radius, introduced by Rota in the early 1960s...

that may be represented over a given field F {\displaystyle F} ; Rota's conjecture describes a possible characterization for every finite field. The...

combinatorics, the proof of the Dowling–Wilson conjecture for geometric lattices, the proof of the Heron–Rota–Welsh conjecture for matroids, the development of the...

F. Geelen, A. M. H. Gerards and A. Kapoor for the GF(4) case of Rota's conjecture on matroid minors. Bertrand Guenin for a forbidden minor characterization...

their chromatic number. The Dinitz theorem is also related to Rota's basis conjecture. Erdős, P.; Rubin, A. L.; Taylor, H. (1979). "Choosability in graphs"...

the foundations of combinatorics by proving a conjecture of Gian–Carlo Rota; in proving Rota's conjecture, Folkman characterized the structure of the homology...

realizable over these fields, part of a family of results codified by Rota's conjecture. The regular matroids are the matroids that can be defined from a...

Geelen, Jim; Gerards, Bert; Whittle, Geoff (Aug 17, 2014), "Solving Rota's conjecture" (PDF), Notices of the American Mathematical Society, 61 (7): 736–743...

a finite set of minimums of finite collections of polynomials. Rota's basis conjecture: for matroids of rank n {\displaystyle n} with n {\displaystyle...

and only if it can be represented by a totally unimodular matrix. Rota's conjecture states that, for every finite field F, the F-linear matroids can be...

etc. For this reason, uniform matroids play an important role in Rota's conjecture concerning the forbidden minor characterization of the matroids that...

co-authors A. M. H. Gerards, and A. Kapoor for their research on Rota's excluded minors conjecture. In 2006, he won the Coxeter–James Prize presented by the...

the proof of the graph minors theorem. Two articles proving Kneser's conjecture, the first by László Lovász and the other by Imre Bárány, appeared back-to-back...

of colors chosen as part of a matroid basis. Bipartite matroid Rota's basis conjecture Zaslavsky, Thomas (1992), "Strong Tutte functions of matroids and...

proven that remain elusive in the more general case. An example is Rota's basis conjecture, the statement that a set of n disjoint bases in a rank-n matroid...

In joint work with June Huh and Eric Katz, he resolved the Heron–Rota–Welsh conjecture on the log-concavity of the characteristic polynomial of matroids...

method" by Blagojević, Ziegler and Frick leads to counterexamples. Rota's basis conjecture Tverberg, H. (1966), "A generalization of Radon's theorem" (PDF)...

buildings in the design of a wheel. He conjectured that they were games and of the tic-tac-toe variety, and conjectured the rules for the game since no rules...

University of California at Berkeley who proved the Macdonald positivity conjecture for Macdonald polynomials. He received his Ph.D. in 1984 in the Massachusetts...

work with Karim Adiprasito and June Huh, he resolved the Heron–Rota–Welsh conjecture on the log-concavity of the characteristic polynomial of matroids...

Gian-Carlo Rota) of one of the founding papers of the modern umbral calculus. In 1985 he and Herman te Riele disproved the Mertens conjecture. In mathematics...

where his formulations became standard. He left two conjectures, both known as Artin's conjecture. The first concerns Artin L-functions for a linear representation...

was found in 1993. In 2006, Grigori Perelman, who proved the Poincaré conjecture, refused his Fields Medal and did not attend the congress. In 2014, Maryam...

Related to the computability of the joint spectral radius is the following conjecture: "For any finite set of matrices M ⊂ R n × n , {\displaystyle {\mathcal...

theorem Birkhoff's theorem Birkhoff–Kakutani theorem Pierce–Birkhoff conjecture Pierce–Birkhoff ring Poincaré–Birkhoff–Witt theorem Algebraic statistics...

the graph; the Hadwiger conjecture states that this is always at least as large as the chromatic number. The Hadwiger conjecture in combinatorial geometry...

ISBN 978-1-60888-120-8. Rule, Bruce (22 September 2013). "Rebutting Conjecture: Scorpion Reversed Course Just Before Being Lost". IUSSCAA.org. Wikimedia...

of zeroes of the Riemann zeta function. See the article on the Mertens conjecture for more information about the connection between M ( n ) {\displaystyle...