70,230 research outputs found
On Zudilin's q-question about Schmidt's problem
We propose an elemantary approach to Zudilin's q-question about Schmidt's
problem [Electron. J. Combin. 11 (2004), #R22], which has been solved in a
previous paper [Acta Arith. 127 (2007), 17--31]. The new approach is based on a
q-analogue of our recent result in [J. Number Theory 132 (2012), 1731--1740]
derived from q-Pfaff-Saalschutz identity.Comment: 5 page
On continuity of Guo Wuwen function
We show that the functions g and gs introduced by Guo Wuwen in [4] are
continuous and semialgebraic. We use this fact to prove that the set Nn of
ordered n-tuples of real numbers, realizable by nonnegative matrices, is a
closed set
Edge Bipartization Faster Than 2^k
In the Edge Bipartization problem one is given an undirected graph and an
integer , and the question is whether edges can be deleted from so
that it becomes bipartite. In 2006, Guo et al. [J. Comput. Syst. Sci.,
72(8):1386-1396, 2006] proposed an algorithm solving this problem in time
; today, this algorithm is a textbook example of an application of
the iterative compression technique. Despite extensive progress in the
understanding of the parameterized complexity of graph separation problems in
the recent years, no significant improvement upon this result has been yet
reported.
We present an algorithm for Edge Bipartization that works in time , which is the first algorithm with the running time dependence on the
parameter better than . To this end, we combine the general iterative
compression strategy of Guo et al. [J. Comput. Syst. Sci., 72(8):1386-1396,
2006], the technique proposed by Wahlstrom [SODA 2014, 1762-1781] of using a
polynomial-time solvable relaxation in the form of a Valued Constraint
Satisfaction Problem to guide a bounded-depth branching algorithm, and an
involved Measure & Conquer analysis of the recursion tree
On 2-adic orders of some binomial sums
We prove that for any nonnegative integers and the binomial sum is divisible by
, where denotes the number of
1's in the binary expansion of . This confirms a recent conjecture of Guo
and Zeng.Comment: 6 page
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