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Odd-order Cayley graphs with commutator subgroup of order pq are hamiltonian
Cayley graph hamiltonian cycle commutator subgroup
2012/5/9
We show that if G is a nontrivial, finite group of odd order, whose commutator subgroup [G,G] is cyclic of order p^m q^n, where p and q are prime, then every connected Cayley graph on G has a hamilton...
The Mobius function of generalized subword order
Chebyshev polynomial discrete Morse theory homotopy type minimal skipped interval Mobius function
2011/9/20
Abstract: Let P be a poset and let P* be the set of all finite length words over P. Generalized subword order is the partial order on P* obtained by letting u \le w if and only if there is a subword u...
The Expected Order of Saturated RNA Secondary Structures
Horton-Strahler number generating function Hankel contour Transfer Theorem singularity analysis
2011/9/9
Abstract: We show the expected order of RNA saturated secondary structures of size $n$ is $\log_4n(1+O(\frac{\log_2n}{n}))$, if we select the saturated secondary structure uniformly at random. Further...
Simplifying and Unifying Bruhat Order for BGB, PGB, KGB, and KGP
Simplifying and Unifying Bruhat Order Representation Theory BGB
2011/8/24
Abstract: This paper provides a unifying and simplifying approach to Bruhat order in which the usual Bruhat order, parabolic Bruhat order, and Bruhat order for symmetric pairs are shown to have combin...
Conjectures of Alperin and Broue for 2-blocks with elementary abelian defect groups of order 8
Conjectures of Alperin Broue for 2-blocks elementary abelian defect groups of order 8
2011/2/21
Using the classification of finite simple groups, we prove Alperin’s weight conjecture
and the character theoretic version of Brou´e’s abelian defect conjecture for 2-blocks of finite groups wi...
Quasi-Permutation Representations of Groups of Order 64
Quasi-permutation representations 2-groups Character theory
2010/2/25
In [1], we gave algorithms to calculate c(G), q(G) and p(G) for a finite group G. In this paper, we will calculate c(G), q(G), p(G) for non-abelian groups G, where |G|=64.