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Combinatorial Results for Semigroups of Order-Preserving Full Transformations
AbstractLet On be the semigroup of all order-preserving full transformations of a finite chain, say Xn = {1, 2, ..., n}, and for a given full transformation α: Xn → Xn let f(α) = |{x ∈ Xn: xα = x}|.Expand
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Asymptotic Results for Semigroups of Order-Preserving Partial Transformations
ABSTRACT Let 𝒫 𝒞 n be the semigroup of all decreasing and order-preserving partial transformations of an n-element chain, and let E(𝒫 𝒞 n ) be its set of idempotents. Among other results,Expand
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Combinatorial results for semigroups of order-preserving partial transformations
Abstract Let PO n be the semigroup of all order-preserving partial transformations of a finite chain. It is shown that | PO n |=c n satisfies the recurrence (2n−1)(n+1)c n+1 =4 3n 2 −1 c nExpand
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Combinatorial Results for the Symmetric Inverse Semigroup
In this note we obtain and discuss formulae for the number of partial one-one transformations (of an n-element set) of height (equivalently, width) r and having exactly k fixed points. Moreover, weExpand
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Classroom note: A Generalization of Leibniz rule for higher derivatives
This note provides a simple method to extend the usual Leibniz rule for higher derivatives of the product of two functions to several functions, which is within the reach of freshman calculusExpand
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On Certain Finite Semigroups of Order-decreasing Transformations I
Let $D_n $ (${\cal O}_n$) be the semigroup of all finite order-decreasing (order-preserving) full transformations of an $n$-element chain, and let $D(n,r) = \{\alpha\in D_n: |\mbox{Im}\alpha| \leqExpand
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On lifts of irreducible 2-Brauer characters of solvable groups
Let be a finite group. Write| | = , where is a prime number and ( ) = 1, and letQ = Q( 2π / ), the field generated by2π / over the fieldQ of rationals. Recall that an ordinary character χ of is saidExpand
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On the Number of Nilpotents in the Partial Symmetric Semigroup
Abstract In this note, we obtain and discuss formulae for the total number of nilpotent partial and nilpotent partial one–one transformations of a finite set.
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Combinatorial Results for Semigroups of Order-Decreasing Partial Transformations
Let PCn be the semigroup of all decreasing and order-preserving partial transformations of a flnite chain. It is shown that jPCnj = rn, where rn is the large (or double)
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Polynomial solutions of differential equations
AbstractA new approach for investigating polynomial solutions of differential equations is proposed. It is based on elementary linear algebra. Any differential operator of the formExpand
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