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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

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 Xn = {1 < 2 …< n}, where p is the only fixed point in α, for some given p ∈Xn, denoted by On,p. This semigroup is nilpotent. In particular, the semigroup On,1 (i.e. p = 1) is already well studied, since it is the maximal nilpotent subsemigroup of the Catalan monoid. But the semigroup On,p is still not well studied for p > 1 except of p = n since On,n is isomorphic to On,1. We determine the rank of On,p (it is Cp-1Cn-p – Cp-2Cn-p-1) and give a presentation of On,p in (Cn-1 – Cn-2) generators and (1 + Cn-1 – Cn-2)(Cn-1 – Cn-2) relations. We illustrate the result for n = 4.


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


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
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