Itamar Stein
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The algebra of the monoid of order-preserving functions on an n-set and other reduced E-Fountain semigroups Open
With every reduced E -Fountain semigroup S which satisfies the generalized right ample condition we associate a category with zero morphisms $$\mathcal {C}(S)$$ . Under some assumptions we prove an isomorphism of $$\Bbbk $$ -algebras $$\Bb…
Representation theory of monoids consisting of order-preserving functions and order-reversing functions on an n-set Open
Let $\operatorname{OD}_{n}$ be the monoid of all order-preserving functions and order-reversing functions on the set $\{1,\ldots,n\}$. We describe a quiver presentation for the monoid algebra $\Bbbk\operatorname{OD}_{n}$ where $\Bbbk$ is a…
The algebra of the monoid of order-preserving functions on an $n$-set and other reduced $E$-Fountain semigroups Open
With every reduced $E$-Fountain semigroup $S$ which satisfies the generalized right ample condition we associate a category with zero morphisms $\mathcal{C}(S)$. Under some assumptions we prove an isomorphism of $\Bbbk$-algebras $\Bbbk S\s…
Algebras of reduced $E$-Fountain semigroups and the generalized ample identity II Open
We study the generalized right ample identity, introduced by the author in a previous paper. Let $S$ be a reduced $E$-Fountain semigroup which satisfies the congruence condition. We can associate with $S$ a small category $\mathcal{C}(S)$ …
Algebras of Reduced $E$-Fountain Semigroups and the Generalized Ample Identity Open
Let $S$ be a reduced $E$-Fountain semigroup. If $S$ satisfies the congruence condition, there is a natural construction of a category $\mathcal{C}$ associated with $S$. We define a $\Bbbk$-module homomorphism $φ:\Bbbk S\to\Bbbk\mathcal{C}$…
Diamond Subgraphs in the Reduction Graph of a One-Rule String Rewriting System Open
In this paper, we study a certain case of a subgraph isomorphism problem. We consider the Hasse diagram of the lattice M k (the unique lattice with k + 2 elements and one anti-chain of length k) and find the maximal k for which it is isomo…
Ehresmann Semigroups Whose Categories are EI and Their Representation\n Theory : Extended Version Open
We study simple and projective modules of a certain class of Ehresmann\nsemigroups, a well-studied generalization of inverse semigroups. Let $S$ be a\nfinite right (left) restriction Ehresmann semigroup whose corresponding\nEhresmann categ…
Ehresmann Semigroups Whose Categories are EI and Their Representation Theory : Extended Version Open
We study simple and projective modules of a certain class of Ehresmann semigroups, a well-studied generalization of inverse semigroups. Let $S$ be a finite right (left) restriction Ehresmann semigroup whose corresponding Ehresmann category…
Ehressman Semigroups Whose Categories are EI and Their Representation Theory Open
We study simple and projective modules of a certain class of Ehresmann semigroups, a well-studied generalization of inverse semigroups. Let S be a finite right (left) restriction Ehresmann semigroup whose corresponding Ehresmann category i…
Representation theory of order-related monoids of partial functions as\n locally trivial category algebras Open
In this paper we study the representation theory of three monoids of partial\nfunctions on an $n$-set. The monoid of all order-preserving functions (i.e.,\nfunctions satisfying $f(x)\\leq f(y)$ if $x\\leq y$) the monoid of all\norder-decre…
Representation theory of order-related monoids of partial functions as locally trivial category algebras Open
In this paper we study the representation theory of three monoids of partial functions on an $n$-set. The monoid of all order-preserving functions (i.e., functions satisfying $f(x)\leq f(y)$ if $x\leq y$) the monoid of all order-decreasing…
Number and Continuous Magnitude Processing Depends on Task Goals and Numerosity Ratio Open
A large body of evidence shows that when comparing non-symbolic numerosities, performance is influenced by irrelevant continuous magnitudes, such as total surface area, density, etc. In the current work, we ask whether the weights given to…