58 research outputs found
A Note On The Cross-Sperner Families
No full textLet be a pair of families of , where
. If and hold for all
and , then is
called a Cross-Sperner pair. P. Frankl and Jian Wang introduced the extremal
problem that
-,
where . In this note, we prove that
for all
. This solves an open problem proposed by P. Frankl and Jian Wang.Comment: We solve an open problem proposed by P. Frankl and Jian Wan
On a conjecture about pattern avoidance of cycle permutations
No full textLet be a cycle permutation that can be expressed as one-line and a cycle form . Archer et al. introduced the notion of pattern avoidance of one-line and all cycle forms for a cycle permutation , defined as and its arbitrary cycle form avoid a given pattern. Let denote the set of cyclic permutations in the symmetric group that avoid in their one-line form and avoid in their all cycle forms. In this note, we prove that is the Pell number for any positive integer . Thereby, we give a positive answer to a conjecture of Archer et al
The full automorphism groups of general position graphs
No full textLet be a non-empty finite set. A flag of is a set of non-empty
proper subsets of such that or for all
. The set is called the type of . Two flags
and are in general position with respect to if or
for all and . For a fixed type , Klaus Metsch
defined the general position graph whose vertices are the flags
of of type with two vertices being adjacent when the corresponding
flags are in general position. In this paper, we characterize the full
automorphism groups of in the case that . In particular,
we solve an open problem proposed by Klaus Metsch.Comment: we solve an open problem proposed by Klaus Metsc
Explore a new book discovery experience in the public library
No full textNowadays, a public library is no longer a place just for the collection of books. It has offered multiple functions to take the responsibility of being a public cultural institution for all citizens. However, in the Netherlands, libraries are losing their members, especially young adults. With the development of technology, a public library is no longer the only choice for books. Libraries are encountering a challenge to attract young people back. They need to strive for providing new kinds of public services to attract this potential new audience.Westfriese Bibliotheken is one of these libraries which has 10 decentralized community libraries in 6 places in the north of the Netherlands. Westfriese Bibliotheken is facing a challenge to reach a bigger group of the generation of youngsters who think a public library is a dull place to go. To narrow down the scope, the book discovery experience for young adults between 18-25 years old was focused. Augmented reality as the technology this project worked with has been proved to benefit the library context.Hence, the objective of this thesis is to explore a new book discovery experience for young adults in the public library in Stede Broec.From the theoretical study (chapter 2) about the book discovery behavior, the behavior pattern was investigated and worked as the design requirements. User research (chapter 3) was conducted to understand the current book discovery experience in the context through contextmapping. It discovered users' concerns and expectations about the book discovery experience. Moreover, the opportunity of this project: designing a new book discovery experience to facilitate serendipity was concluded based on user research findings. Under the framework of the serendipity theory (chapter 4), design opportunities for facilitating serendipity in the current library were gathered. The study on augmented reality (chapter 5) helped to define design qualities and technologies that this project can make use of.With the research insights, a design goal with three design qualities (fascinating, playful, and inviting) and relevant design requirements were formulated (chapter 6). They contributed as a guideline to the design solution.Ideas were gathered through a creative session and based on these ideas three initial concepts were generated. Concepts were evaluated and iterated with users, clients, and fellow students. The final design outcome is a phone-based AR application with two main parts: exploring and browsing parts. It offers both basic and additional information about books to stimulate users to experience serendipity in the public library. Finally, an evaluation test was conducted to validate if the final design can fulfill the design goal. The final design achieves a good usability and desirability performance evaluated by 6 participants in the library. The evaluation test demonstrated that the additional information about books and interaction between the physical and digital world can let users feel fascinated, invited, and playful during the book discovery experience.Design for Interactio
Sign-Balanced Pattern-Avoiding Permutation Classes
No full textA set of permutations is called sign-balanced if the set contains the same
number of even permutations as odd permutations. Let be the set of permutations in the symmetric group
which avoids patterns . The aim of this
paper is to investigate when, for certain patterns , is sign-balanced for
every integer . We prove that for any , if is
sign-balanced except , then is sign-balanced for every integer . In addition, we
give some results in the case of avoiding some patterns of length
On the permutations that strongly avoid the pattern 312 or 231
No full textIn 2019, B\'ona and Smith introduced the notion of \emph{strong pattern
avoidance}, that is, a permutation and its square both avoid a given pattern.
In this paper, we enumerate the set of permutations which not only
strongly avoid the pattern or but also avoid the pattern ,
for and some . One of them is to give a positive
answer to a conjecture of Archer and Geary
Investigation into the Promotion and Instruction of Chinese Traditional Music in Liaocheng Peiwen School of Peking University
No full textThis research investigates the promotion and instruction of Chinese Traditional music in Liaocheng Peiwen School of Peking University. The first author, an alum with a decade of pedagogical experience, examined the challenges faced by private schools in providing tailored regulatory frameworks for Chinese Traditional music education. We share practical experience, drawing on the successful establishment of the school-based course "Chinese Folk Music and Geography." As the course is offered each year during the geography exam for students in their second year of junior high school, singing folk songs while learning geography enables students to explore China's beautiful landscapes while broadening their horizons. Students can understand the connection between folk music and geography, assisting their preparation for the exam
Simulation Based Value-at-Risk for High-dimensional Nonlinear Portfolios
No full textChen, Junyao.Thesis M.Phil. Chinese University of Hong Kong 2016.Includes bibliographical references (leaves ).Abstracts also in Chinese.Title from PDF title page (viewed on …)
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