We survey known results and open problems in abelian combinatorics on words. Abelian
combinatorics on words is the extension to the commutative setting of the classical theory of …

The block reversal of a word is a generalization of the concept of reversal of a word where in
place of reversing individual letters, we take the blocks of the word in the reverse order …

An absent factor of a string w is a string u which does not occur as a contiguous substring
(aka factor) inside w. We extend this well-studied notion and define absent subsequences: a …

I will show that there exist two binary words (one of length 4 and one of length 6) that play a
special role in many different problems in combinatorics on words. They can therefore be …

In the literature, many bijections between (labeled) Motzkin paths and various other
combinatorial objects are studied. We consider abelian (un) bordered words and show the …

Abstract In 1999 Lyngsø and Pedersen proposed a conjecture stating that every binary
circular word of length n with equal number of zeros and ones has an antipalindromic linear …

A word u is a scattered factor of w if u can be obtained from w by deleting some of its letters.
That is, there exist the (potentially empty) words u_1, u_2,..., u_n, and v_0, v_1,.., v_n such …

In the literature, many bijections between (labeled) Motzkin paths and various other
combinatorial objects are studied. We consider abelian (un) bordered words and show the …

An n-ary word is called minimal-palindromic if it does not contain palindromic subwords of
length greater than⌈| w| n⌉. The MP-ratio of a given n-ary word w is defined as the quotient …

Traditionally in combinatorics on words one studies unavoidable regularities that appear in
sufficiently long strings over a fixed size alphabet. Inspired by permutation problems …