Search results for "102"
showing 10 items of 2892 documents
Forests and pattern-avoiding permutations modulo pure descents
2018
Abstract We investigate an equivalence relation on permutations based on the pure descent statistic. Generating functions are given for the number of equivalence classes for the set of all permutations, and the sets of permutations avoiding exactly one pattern of length three. As a byproduct, we exhibit a permutation set in one-to-one correspondence with forests of ordered binary trees, which provides a new combinatorial class enumerated by the single-source directed animals on the square lattice. Furthermore, bivariate generating functions for these sets are given according to various statistics.
A counterexample to Feit's Problem VIII on decomposition numbers
2016
We find a counterexample to Feit's Problem VIII on the bound of decomposition numbers. This also answers a question raised by T. Holm and W. Willems.
Character restrictions and multiplicities in symmetric groups
2017
Abstract We give natural correspondences of odd-degree characters of the symmetric groups and some of their subgroups, which can be described easily by restriction of characters, degrees and multiplicities.
Extending the star order to Rickart rings
2015
Star partial order was initially introduced for semigroups and rings with (proper) involution. In particular, this order has recently been studied on Rickart *-rings. It is known that the star order in such rings can be characterized by conditions not involving involution explicitly. Owing to these characterizations, the order can be extended to certain special Rickart rings named strong in the paper; this extension is the objective of the paper. The corresponding order structure of strong Rickart rings is studied more thoroughly. In particular, the most significant lattice properties of star-ordered Rickart *-rings are successfully transferred to strong Rickart rings; also several new resu…
Tighter Relations between Sensitivity and Other Complexity Measures
2014
The sensitivity conjecture of Nisan and Szegedy [12] asks whether the maximum sensitivity of a Boolean function is polynomially related to the other major complexity measures of Boolean functions. Despite major advances in analysis of Boolean functions in the past decade, the problem remains wide open with no positive result toward the conjecture since the work of Kenyon and Kutin from 2004 [11].
Brauer’s Height Zero Conjecture for principal blocks
2021
Abstract We prove the other half of Brauer’s Height Zero Conjecture in the case of principal blocks.
Search by Quantum Walks on Two-Dimensional Grid without Amplitude Amplification
2013
We study search by quantum walk on a finite two dimensional grid. The algorithm of Ambainis, Kempe, Rivosh [AKR05] uses \(O(\sqrt{N \log{N}})\) steps and finds a marked location with probability O(1 / logN) for grid of size \(\sqrt{N} \times \sqrt{N}\). This probability is small, thus [AKR05] needs amplitude amplification to get Θ(1) probability. The amplitude amplification adds an additional \(O(\sqrt{\log{N}})\) factor to the number of steps, making it \(O(\sqrt{N} \log{N})\).
On σ-subnormal closure
2020
Let σ={σi:i∈I} be a partition of the set P of all prime numbers. A subgroup A of a finite group G is called σ-subnormal in G if there is a chain of subgroups A=A0⊆A1⊆⋯⊆An=G with Ai−1 normal in Ai o...
On complements of 𝔉-residuals of finite groups
2016
ABSTRACTA formation 𝔉 of finite groups has the generalized Wielandt property for residuals, or 𝔉 is a GWP-formation, if the 𝔉-residual of a group generated by two 𝔉-subnormal subgroups is the subgroup generated by their 𝔉-residuals. The main aim of the paper is to determine some sufficient conditions for a finite group to split over its 𝔉-residual.
Characters and Sylow 2-subgroups of maximal class revisited
2018
Abstract We give two ways to distinguish from the character table of a finite group G if a Sylow 2-subgroup of G has maximal class. We also characterize finite groups with Sylow 3-subgroups of order 3 in terms of their principal 3-block.