In this paper the automorphism group of two posets, Dk,n and Bm,n is determined. Dk,n is the poset of DNA strands of length at most n, built up with k complement pairs of letters, and partially ordered by the subsequence relation. Bm,n is the set of all subsequences of the word um,n = a1...an defined over the alphabet {0, 1, ..., (m−1)}, where ai ≡ i (mod m). The automorphism group of Bm,n was ...

We develop the relationship between minimal transitive star factorizations and noncrossing partitions. This gives a new combinatorial proof of result by Irving Rattan, specialization Kreweras. It also arises in poset on symmetric group whose definition is motivated Subword Property Bruhat order.

Muscle atrophy (cachexia) in cancer patients is a life-threatening condition for which therapeutic options are limited. Zhou et al. (2010) now identify a new target for treating cachexia, the activin type-2 receptor (ActRIIB). In several mouse models of cachexia, the authors reversed wasting of skeletal and cardiac muscle and increased life span by blocking ActRIIB with a decoy receptor.

Recently we introduced and studied the shadow minimization problem under word-subword relation. In this paper we consider this problem for the restricted case and give optimal solution.

We study free profinite subgroups of free profinite semigroups of the same rank using, as main tools, iterated implicit operators, subword complexity and the associated entropy.