Konrad Pióro

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The symmetric group S(n) is partially ordered by Bruhat order. This order is extended by L. In this paper we show that Renner order can be also defined for sets of all functions, partial functions, injective and partial injective functions from {1, we generalize Fortin's results on these posets, and also, using simple facts and methods of linear algebra, we(More)
We investigate finite commutative groupoids G = 〈G, ◦〉 such that g ◦ h 6= g for all elements g, h of G. First, we show that for any such groupoid, its weak (i.e. partial) subgroupoid lattice uniquely determines its subgroupoid lattice. Next, we characterize the lattice of all weak subgroupoids of such a groupoid. This is a distributive finite lattice(More)
Necessary and sufficient conditions will be found for quadruples of lattices to be isomorphic to lattices of weak, relative, strong subalgebras and initial segments, respectively, of one partial unary algebra. To this purpose we will start with a characterization of pairs of lattices that are weak and strong subalgebra lattices of one partial unary algebra,(More)
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