A classical theorem of Edmonds provides a min-max formula relating the maximal size of a
set in the intersection of two matroids to a “covering" parameter. We generalize this theorem …

A formula for Glynn's hyperdeterminant \det_p (p prime) of a square matrix shows that the
number of ways to decompose any integral doubly stochastic matrix with row and column …

In 1989, Rota made the following conjecture. Given bases in an-dimensional vector space,
one can always find disjoint bases of, each containing exactly one element from each (we …

Rota's Basis Conjecture is a well known problem from matroid theory, that states that for any
collection of $ n $ bases in a rank $ n $ matroid, it is possible to decompose all the elements …

Rota’s Basis Conjecture for Paving Matroids Page 1 SIAM J. DISCRETE MATH. c 2006 Society
for Industrial and Applied Mathematics Vol. 20, No. 4, pp. 1042–1045 ROTA’S BASIS …

':~ DISCRETE MATHEMATICS Page 1 ':~ DISCRETE MATHEMATICS ELSEVIER Discrete
Mathematics 146 (1995) 299-302 Note An exchange property of matroid Wendy Chan …

Abstract Gian-Carlo Rota conjectured that for any $ n $ bases $ B_1, B_2,\ldots, B_n $ in a
matroid of rank $ n $, there exist $ n $ disjoint transversal bases of $ B_1, B_2,\ldots, B_n …

In 1989, Rota conjectured that, given n bases B 1,…, B n of the vector space F n over some
field F, one can always decompose the multi-set B 1∪⋯∪ B n into transversal bases. This …

The Alon--Tarsi Latin squares conjecture is extended to odd dimensions by stating it for
reduced Latin squares (Latin squares having the identity permutation as their first row and …

Let M1 and M2 be two matroids on the same ground set S. We conjecture that if there do not
exist disjoint subsets A1, A2,…, Ak+ 1 of S, such that [Formula: see text], and similarly for M2 …