Topics on Combinatorial Semigroups

By combinatorial semigroups, we mean a general term of concepts, facts and methods which are produced in investigating of algebraic and combinatorial properties, constructions, classifications and interrelations of formal languages and automata, codes, finite and infinite words by using semigroup theory and combinatorial analysis. The main research objects in this field are the elements and subsets of the free semigroups and monoids and many combinatorial properties of these objects, which are closely related to algebraic theory of semigroups.

This book first introduces some basic concepts and notations in combinatorial semigroups. Since many contents involving the constructions of (generalized) disjunctive languages and regular languages are closely related to the algebraic theory of codes, some selected topics are introduced in the following chapter, including the method of defining codes by using dependence systems, the maximality and completeness of codes, and the detailed discussion of some special kinds of codes such as convex codes, semaphore codes and solid codes. Then the remaining chapters present the main topics of the book - regular languages, disjunctive languages, and their various kinds of generalizations.

This book might be useful to researchers in mathematics who are interested in combinatorial semigroups.

Prof. Yuqi Guo graduated from Fudan University in July 1964, and then worked in Department of Mathematics of Lanzhou University until February 1994. In June 1986, he was approved as a doctoral supervisor. He once served as the head of Department of Mathematics of Lanzhou University and the chairman of Mathematics Society of Gansu. After 1994, he worked in Department of Mathematics of Yunnan University and Southwest University, and served as the director of Department of Mathematics, the dean of School of Science of Yunnan University and the director of Institute of Mathematics of Southwest University, and then, back in Lanzhou University and has been teaching in Cuiying College and School of Mathematics and Statistics of Lanzhou University since 2012. In addition to undergraduate teaching, he has been engaged in academic research and high-level talent training of semigroups and combinatorial semigroups. He has presided eight projects of National Natural Science Foundation of China and published more than eighty academic papers. He has won the first prize of Provincial and Ministerial Natural Science Award of China in 1997 and the national excellent award of teaching achievements in colleges and universities in 1989. Thirty-three doctors and more than eighty masters have been trained.

Prof. Yun Liu graduated from Sun Yat-sen University in 2006. He has worked in Department of Mathematics of Yuxi Normal University since July 2003 and was promoted to Professor in 2012. Now he is a Young and Middle-aged Academic and Technical Leader of Yunnan and Yuxi, a member of the Mathematics Teaching Steering Committee of Yunnan colleges and universities, a director of Mathematics Society of Yunnan, an executive director of Applied Statistics Society of Yunnan. He has presided two projects of National Natural Science Foundation of China and published more than twenty academic papers.

Prof. Shoufeng Wang graduated from Southwest University in 2010. He has worked in School of Mathematics of Yunnan Normal University since July 2005 and was promoted to Professor in 2017. He has presided three projects of National Natural Science Foundation of China and published more than 40 academic papers. He has been a master supervisor of Yunnan Normal University since 2014.