The next meeting of the Algebra and Logic Seminar will be held on **October 21, 2022** (Friday) **at 1:00 pm (UTC+2)** online in Zoom.

A talk on:

**Ranks and Presentations for Order-Preserving Transformations with One Fixed Point**

**Ranks and Presentations for Order-Preserving Transformations with One Fixed Point**

will be delivered by **Jörg Koppitz (joint work with S. Worawiset).**

**Abstract. **We consider the semigroup (no monoid) of all order-preserving full transformations α on an n-element chain X_{n} = {1 < 2 …< n}, where p is the only fixed point in α, for some given p ∈X_{n}, denoted by O_{n,p}. This semigroup is nilpotent. In particular, the semigroup O_{n,1} (i.e. p = 1) is already well studied, since it is the maximal nilpotent subsemigroup of the Catalan monoid. But the semigroup O_{n,p} is still not well studied for p > 1 except of p = n since O_{n,n} is isomorphic to O_{n,1}. We determine the rank of O_{n,p} (it is C_{p-1}C_{n-p} – C_{p-2}C_{n-p-1}) and give a presentation of O_{n,p} in (C_{n-1} – C_{n-2}) generators and (1 + C_{n-1} – C_{n-2})(C_{n-1} – C_{n-2}) relations. We illustrate the result for n = 4.

The seminar will be held online. Join the Zoom link:

https://us02web.zoom.us/j/

Topic: Онлайн семинар на секция “Алгебра и логика”

Time: Oct 21, 2022 01:00 PM Sofia

Meeting ID: 851 3737 5021

Passcode: 035647

Algebra and Logic Department, IMI – BAS

http://www.math.bas.bg/algebra/seminarAiL/

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