Begin with the generating function for unrestricted partitions:
Now change some of the plus signs to minus signs. The resulting series will have coefficients congruent, mod 2, to the coefficients of the generating series for unrestricted partitions. I conjecture that the signs may be chosen such that all the coefficients of the series are either 1, -1, or zero.
For let denote the minimal number such that there is a rainbow in every equinumerous -coloring of for every
The deck of a graph is the multiset consisting of all unlabelled subgraphs obtained from by deleting a vertex in all possible ways (counted according to multiplicity).
Conjecture 1 In the couples problem, if the acceptability graph is a tree, then a stable matching exists for any set of preference lists.
The problem is to give a characterization of the pairs whose tensor product is robust.
Keywords: algebraic independence
Beneš Conjecture ★★★
Given a partition of a finite set , stabilizer of , denoted , is the group formed by all permutations of preserving each block in .
In particular, what about the sequence , where is a permutation of ?
A connected simple graph is called double-critical, if removing any pair of adjacent vertexes lowers the chromatic number by two.