scholarly journals Fully Packed Loop Configurations: Polynomiality and Nested Arches

10.37236/6963 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Florian Aigner
Keyword(s):  
Vector Space ◽  
Polynomial Function ◽  
General Setting ◽  
Partial Result ◽  
Link Pattern

This article proves a conjecture by Zuber about the enumeration of fully packed loops (FPLs). The conjecture states that the number of FPLs whose link pattern consists of two noncrossing matchings which are separated by $m$ nested arches is a polynomial function in $m$ of certain degree and with certain leading coefficient. Contrary to the approach of Caselli, Krattenthaler, Lass and Nadeau (who proved a partial result) we make use of the theory of wheel polynomials developed by Di Francesco, Fonseca and Zinn-Justin. We present a new basis for the vector space of wheel polynomials and a polynomiality theorem in a more general setting. This allows us to finish the proof of Zubers conjecture.

scholarly journals Halfway to Rota’s Basis Conjecture

2020 ◽  
Vol 2020 (21) ◽  
pp. 8007-8026 ◽  
Author(s):  
Matija Bucić ◽  
Matthew Kwan ◽  
Alexey Pokrovskiy ◽  
Benny Sudakov
Keyword(s):  
Vector Space ◽  
General Setting ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
The Subject

Abstract In 1989, Rota made the following conjecture. Given $n$ bases $B_{1},\dots ,B_{n}$ in an $n$-dimensional vector space $V$, one can always find $n$ disjoint bases of $V$, each containing exactly one element from each $B_{i}$ (we call such bases transversal bases). Rota’s basis conjecture remains wide open despite its apparent simplicity and the efforts of many researchers (e.g., the conjecture was recently the subject of the collaborative “Polymath” project). In this paper we prove that one can always find $\left (1/2-o\left (1\right )\right )n$ disjoint transversal bases, improving on the previous best bound of $\Omega \left (n/\log n\right )$. Our results also apply to the more general setting of matroids.

On Semi - Pre irresolute Topological Vector Space

2018 ◽  
Vol 14 (3) ◽  
pp. 184-192
Author(s):  
Radhi Ali ◽  
◽  
Jalal Hussein Bayati ◽  
Suhad Hameed
Keyword(s):  
Vector Space ◽  
Topological Vector Space

Aplikasi Deteksi Kemiripan Tugas Paper

2017 ◽  
Vol 15 (2) ◽  
pp. 5
Author(s):  
Anthony Anggrawan ◽  
Azhari
Keyword(s):  
Information Retrieval ◽  
Vector Space ◽  
Vector Space Model ◽  
Mean Average Precision ◽  
Average Precision ◽  
Information Searching ◽  
Space Model ◽  
Model Method

Information searching based on users’ query, which is hopefully able to find the documents based on users’ need, is known as Information Retrieval. This research uses Vector Space Model method in determining the similarity percentage of each student’s assignment. This research uses PHP programming and MySQL database. The finding is represented by ranking the similarity of document with query, with mean average precision value of 0,874. It shows how accurate the application with the examination done by the experts, which is gained from the evaluation with 5 queries that is compared to 25 samples of documents. If the number of counted assignments has higher similarity, thus the process of similarity counting needs more time, it depends on the assignment’s number which is submitted.

Unifying Bayesian Inference and Vector Space Models for Improved Decipherment

2015 ◽  
Author(s):  
Qing Dou ◽  
Ashish Vaswani ◽  
Kevin Knight ◽  
Chris Dyer
Keyword(s):  
Bayesian Inference ◽  
Vector Space ◽  
Vector Space Models

Aplikasi Rekomendasi Buku Pada Katalog Perpustakaan Universitas Multimedia Nusantara Menggunakan Vector Space Model

2018 ◽  
Vol 9 (2) ◽  
pp. 97-105
Author(s):  
Richard Firdaus Oeyliawan ◽  
Dennis Gunawan
Keyword(s):  
Vector Space ◽  
Vector Space Model ◽  
Vector Model ◽  
Library Management ◽  
Space Model ◽  
Library Management System ◽  
Index Terms ◽  
Library Catalogue ◽  
Language Sample ◽  
F Measure

Library is one of the facilities which provides information, knowledge resource, and acts as an academic helper for readers to get the information. The huge number of books which library has, usually make readers find the books with difficulty. Universitas Multimedia Nusantara uses the Senayan Library Management System (SLiMS) as the library catalogue. SLiMS has many features which help readers, but there is still no recommendation feature to help the readers finding the books which are relevant to the specific book that readers choose. The application has been developed using Vector Space Model to represent the document in vector model. The recommendation in this application is based on the similarity of the books description. Based on the testing phase using one-language sample of the relevant books, the F-Measure value gained is 55% using 0.1 as cosine similarity threshold. The books description and variety of languages affect the F-Measure value gained. Index Terms—Book Recommendation, Porter Stemmer, SLiMS Universitas Multimedia Nusantara, TF-IDF, Vector Space Model

DISTANCE EDUCATION IN FURTHER PROFESSIONAL TRAINING IN ENTERPRISES DURING PANDEMIC PERIOD

2020 ◽  
Author(s):  
Marta Matulčíková ◽  
Daniela Breveníková
Keyword(s):  
Distance Education ◽  
Empirical Research ◽  
Management System ◽  
Professional Training ◽  
Developmental Stages ◽  
Content Management ◽  
Partial Result ◽  
Corporate Education ◽  
Research Survey ◽  
Learning Management

Constraints on our personal and professional life imposed by the COVID 19 pandemic have radically influenced our approach to forms of education, including those used in further professional training of employees. This shift means the focus on distance education as a managed educational form, which is suitable for further professional training. The aim of the paper is to present the implementation of distance education in further professional training in enterprises and based on the empirical research propose ways of improving options of education. Distance education is characterised in terms of its principles and developmental stages. Its first generation was correspondence education. The Learning Management System (LMS) and Learning Content Management System (LCMS) are described as the systems applied in further professional training. The research was conducted by means of the questionnaire method, combined with the pre-research survey. Results of empirical research are presented in tables. Separate parts of the paper deal with ICT application in corporate education (correspondence education, Computer-based training (CBT), Web-based training (WBT), Technology Based Training (TBT) and with the utilisation of Learning Management Systems (LMS). Analysis of respondent opinions shows that respondents tend to prefer the face-to-face form of corporate education. The length of the pandemic is going to affect the spread of e-learning in corporate education and its role in education. The learners’ interest may be expected to be shifted to LCM and LCMS utilisation. The paper is a partial result of the research scheme VEGA No. 1/0309/18 “Social networks in human resource management” supported by the Ministry of Education, Science and Research and Sports, Slovakia

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

Modeling Interferometric Structures with Birefringent Elements: A Linear Vector-Space Formalism

2013 ◽  
Author(s):  
Nicholas J. Frigo ◽  
Vincent J. Urick ◽  
Frank Bucholtz
Keyword(s):  
Vector Space ◽  
Linear Vector ◽  
Space Formalism ◽  
Linear Vector Space

First Movers and Follow-on Invention: Evidence from a Vector Space Model of Invention

2019 ◽  
Author(s):  
Kenneth A. Younge ◽  
Jeffrey M. Kuhn
Keyword(s):  
Vector Space ◽  
Vector Space Model ◽  
Space Model
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