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Results tagged with co.combinatorics
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user 120914
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
20
votes
1
answer
977
views
Proof of CFSG assuming every simple group is two-generated
It is well-known that one of the corollaries of the classification of finite simple groups (CFSG) is that every finite simple group can be generated by two elements. In a comment on an answer to an ol …
13
votes
Conceptual reason why the sign of a permutation is well-defined?
Obviously, there are lots of answers already, but I thought I'd give the proof of (5) as given by Jordan already in 1870 in his Traité des substitutions -- this has the benefit of being quite clear to …
1
vote
Accepted
(Translation request) Hypotheses of the Blom-Fredberg bounds on denumerants?
The article is [Blom, G. and Fröberg, C-E., Om Myntväxling, Nordisk Matematisk Tidskrift, 1962, Vol. 10, No. 1/2 (1962), pp. 55-69] for anyone who wishes to sing along.
After reading through the artic …
13
votes
Accepted
Transposition Cayley graphs are planar
You already have an answer regarding the first part of your question, but this uses the fact that with your given generating set, the Cayley graph is $(n-1)$-regular. What if we pick the generating se …
4
votes
super Lyndon words
An article you probably want to look at is E. S. Chibrikov, "The Right-Normed Basis for a Free Lie Superalgebra and Lyndon–Shirshov Words", Algebra Logika 45 (2006), issue 4, pp. 458--483. This contai …
3
votes
Accepted
Extension of chromatic polynomial to multi graphs
I think that the Tutte polynomial, as suggested by Fedor Petrov in the comments, is likely what you are looking for. For a graph $G$, this is the polynomial $$ T(x, y) = \sum_{A \subseteq E(G)} (x-1)^ …