离散数学期刊(英文)最新文献_第4页

Toric Heaps, Cyclic Reducibility, and Conjugacy in Coxeter Groups Coxeter群中的Toric堆、循环可还原性和共轭性

离散数学期刊(英文) Pub Date : 2019-09-18 DOI: 10.4236/ojdm.2019.94010

Shi Chao, M. Macauley

{"title":"Toric Heaps, Cyclic Reducibility, and Conjugacy in Coxeter Groups","authors":"Shi Chao, M. Macauley","doi":"10.4236/ojdm.2019.94010","DOIUrl":"https://doi.org/10.4236/ojdm.2019.94010","url":null,"abstract":"In 1986, G.X. Viennot introduced the theory of heaps of pieces as a visualization of Cartier and Foata’s “partially commutative monoids”. These are essentially labeled posets satisfying a few additional properties, and one natural setting where they arise is as models of reduced words in Coxeter groups. In this paper, we introduce a cyclic version of a heap, which loosely speaking, can be thought of as taking a heap and wrapping it into a cylinder. We call this object a toric heap, because we formalize it as a labeled toric poset, which is a cyclic version of an ordinary poset. Defining the category of toric heaps leads to the notion of certain morphisms such as toric extensions. We study toric heaps in Coxeter theory, because a cyclic shift of a reduced word is simply a conjugate by an initial or terminal generator. As such, we formalize and study a framework that we call cyclic reducibility in Coxeter theory, which is closely related to conjugacy. We introduce what it means for elements to be torically reduced, which is a stronger condition than simply being cyclically reduced. Along the way, we encounter a new class of elements that we call torically fully commutative (TFC), which are those that have a unique cyclic commutativity class, and comprise a strictly bigger class than the cyclically fully commutative (CFC) elements. We prove several cyclic analogues of results on fully commutative (FC) elements due to Stembridge. We conclude with how this framework fits into recent work in Coxeter groups, and we correct a minor flaw in a few recently published theorems.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49625410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Generalizations of the Feline and Texas Chainsaw Josephus Problems Feline和Texas Chainsaw Josephus问题的推广

离散数学期刊(英文) Pub Date : 2019-08-09 DOI: 10.4236/ojdm.2019.94011

David Ariyibi, Kevin L. Chang, P. Harris

引用次数: 0

Game Chromatic Number of Some Regular Graphs 若干正则图的游戏色数

离散数学期刊(英文) Pub Date : 2019-08-09 DOI: 10.4236/ojdm.2019.94012

Ramy S. Shaheen, Z. Kanaya, Khaled Alshehada

引用次数: 1

Reconstruction of 2-Convex Polyominoes with Non-Empty Corners 非空角2-凸多项式的重构

离散数学期刊(英文) Pub Date : 2019-08-09 DOI: 10.4236/OJDM.2019.94009

K. Tawbe, S. Mansour

引用次数: 0

The Ordinal Interpretation of the Integers and Its Use in Number Theory 整数的序数解释及其在数论中的应用

离散数学期刊(英文) Pub Date : 2019-08-09 DOI: 10.4236/ojdm.2019.94013

Nathan Hamlin

{"title":"The Ordinal Interpretation of the Integers and Its Use in Number Theory","authors":"Nathan Hamlin","doi":"10.4236/ojdm.2019.94013","DOIUrl":"https://doi.org/10.4236/ojdm.2019.94013","url":null,"abstract":"The author recently published a paper which claimed that an ordinal interpretation of numbers had limited applicability for cryptography. A further examination of this subject, in particular to what extent an ordinal interpretation is useful for recurrence sequences, is needed. Hilbert favored an interpretation of the natural numbers that placed their ordinal properties prior to their cardinal properties [1] [2]. The author examines ordinal uses of the integers in number theory in order to discuss the possibilities and limitations of this approach. The author hopes this paper will be useful in clarifying or even correcting some matters that were discussed in his paper of January of 2018. I was trained informally in philosophical realism, and while I think idealism too has a place, at this time in my life I believe that the weight of evidence and usefulness is more on the side of philosophical materialism. I hope this discussion will help supplement for my readers the material in Number in Mathematical Cryptography. I still maintain that a lack of clarity on these matters has hindered progress in cryptography; and it has taken time for me to better understand these things. I hope others who have interest and ability will assist in making these matters clearer. My intention was to work in pure mathematics, and the transition to an applied mindset was difficult for me. As a result, I feel most comfortable in a more middle-of-the road attitude, but have had to slowly move to a more precise analysis of the physical quantities involved. I hope my readers will be patient with my terminology, which is still evolving, and my discussion of things which are more indirectly related, and which are necessary for my expression. These are important things for the mathematical community to understand, and I hope smarter and more knowledgeable people will address my errors, and improve upon the things I might have correct. I am discussing sequences which are sometimes a use of both ordinal and cardinal numbers.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43797327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Infinite Sets of Solutions and Almost Solutions of the Equation N⋅M = reversal(N⋅M) II 方程N·M=逆（N·M）II的无穷集解和概解

离散数学期刊(英文) Pub Date : 2019-07-08 DOI: 10.4236/OJDM.2019.93007

V. Nitica, Premalata Junius

引用次数: 0

Domination and Eternal Domination of Jahangir Graph Jahangir图的支配与永恒支配

离散数学期刊(英文) Pub Date : 2019-07-08 DOI: 10.4236/OJDM.2019.93008

Ramy S. Shaheen, Mohammad Assaad, Ali Kassem

引用次数: 2

Irreducible Polynomials in Ζ[x] That Are Reducible Modulo All Primes Γ[x]中可约模的不可约多项式

离散数学期刊(英文) Pub Date : 2019-04-02 DOI: 10.4236/OJDM.2019.92006

Shiv Gupta