Publications

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Conference Proceedings
Semigroups and formal languages. Eds. Jorge M. André, V{\'ı}tor H. Fernandes, Mário J. J. Branco, Gracinda M. S. Gomes, John Fountain, and John C. Meakin. Proceedings of the International Conference held at the Universidade de Lisboa, Lisboa, July 12–15, 2005. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007.
Semigroups and languages. Eds. Isabel M. Araújo, Mário J. J. Branco, V{\'ı}tor H. Fernandes, and Gracinda M. S. Gomes. Proceedings of the workshop held at the University of Lisbon, Lisboa, November 27–29, 2002. River Edge, NJ: World Scientific Publishing Co. Inc., 2004.
Journal Article
Araújo, João, Vítor H. Fernandes, Manuel M. Jesus, Victor Maltcev, and James D. Mitchell. "Automorphisms of partial endomorphism semigroups." Publicationes Mathematicae Debrecen. 79.1-2 (2011): 23-39.
André, J. M., V. H. Fernandes, and J. D. Mitchell. "Largest 2-generated subsemigroups of the symmetric inverse semigroup." Proc. Edinb. Math. Soc. (2). 50 (2007): 551-561.Website
Araújo, Isabel M., Mário J. J. Branco, Vitor H. Fernandes, Gracinda M. S. Gomes, and N. Ruškuc. "On generators and relations for unions of semigroups." Semigroup Forum. 63 (2001): 49-62.
Ayık, H., Vítor H. Fernandes, and E. Korkmaz. "On monoids of monotone partial transformations of a finite chain whose domains and ranges are intervals." (Submitted). AbstractWebsite

In this note, we consider the monoid PIM_n of all partial monotone transformations on a chain with n elements whose domains and ranges are intervals and its submonoid IM_n constituted by the full transformations. For both of these monoids, our aim is to determine their cardinalities and ranks and define them by means of presentations. We also calculate the number of nilpotent elements of PIM_n.

Ayık, H., Vítor H. Fernandes, and E. Korkmaz. "On the monoid of partial order-preserving transformations of a finite chain whose domains and ranges are intervals." (Submitted). AbstractWebsite

In this paper, we consider the monoid PIO_n, of all partial order-preserving transformations on a chain with n elements whose domains and ranges are intervals, along with its submonoid PIO_n^- of order-decreasing transformations. Our main aim is to give presentations for PIO_n^- and PIO_n. Moreover, for both monoids, we describe regular elements and determine their ranks, cardinalities and the numbers of idempotents and nilpotents.