Sublattices of a lattice of clones of functions on a 3-element set. I

1999 ◽  
Vol 38 (1) ◽  
pp. 1-11 ◽  
Author(s):  
A. A. Bulatov
Keyword(s):  
Element Set ◽  
Lattice Of Clones

An extension matter element set schema for analogical reasoning

1999 ◽  
Vol 32 (2) ◽  
pp. 8647-8652
Author(s):  
Shunxi Xu ◽  
Xingyu Wang
Keyword(s):  
Analogical Reasoning ◽  
Element Set

ON THE MAXIMAL SUBSEMIGROUPS OF SOME TRANSFORMATION SEMIGROUPS

2008 ◽  
Vol 01 (02) ◽  
pp. 189-202 ◽  
Author(s):  
I. Dimitrova ◽  
J. Koppitz
Keyword(s):  
Transformation Semigroups ◽  
Maximal Subsemigroups ◽  
Element Set

Let Singn be the semigroup of all singular transformations on an n-element set. We consider two subsemigroups of Singn: the semigroup On of all isotone singular transformations and the semigroup Mn of all monotone singular transformations. We describe the maximal subsemigroups of these two semigroups, and study the connections between them.

scholarly journals Period Lengths for Iterated Functions

2010 ◽  
Vol 20 (2) ◽  
pp. 289-298 ◽  
Author(s):  
ERIC SCHMUTZ
Keyword(s):  
Expected Value ◽  
Iterated Functions ◽  
Image Position ◽  
Element Set

Let Ωnbe thenn-element set consisting of all functions that have {1, 2, 3, . . .,n} as both domain and codomain. LetT(f) be the order off,i.e., the period of the sequencef,f(2),f(3),f(4). . . of compositional iterates. A closely related number,B(f) = the product of the lengths of the cycles off, has previously been used as an approximation forT. This paper proves that the average values of these two quantities are quite different. The expected value ofTiswherek0is a complicated but explicitly defined constant that is approximately 3.36. The expected value ofBis much larger:

Hyperclones on a Two-Element Set

2002 ◽  
Vol 8 (4) ◽  
pp. 495-501 ◽  
Author(s):  
HAJIME MACHIDA
Keyword(s):  
Element Set

scholarly journals Some Identities Involving Derangement Polynomials and Numbers and Moments of Gamma Random Variables

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Lee-Chae Jang ◽  
Dae San Kim ◽  
Taekyun Kim ◽  
Hyunseok Lee
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Random Variables ◽  
Natural Extensions ◽  
Element Set

The problem of counting derangements was initiated by Pierre Rémond de Montmort in 1708. A derangement is a permutation that has no fixed points, and the derangement number D n is the number of fixed point free permutations on an n element set. Furthermore, the derangement polynomials are natural extensions of the derangement numbers. In this paper, we study the derangement polynomials and numbers, their connections with cosine-derangement polynomials and sine-derangement polynomials, and their applications to moments of some variants of gamma random variables.

Colorful Partitions of Cardinal Numbers

1979 ◽  
Vol 31 (3) ◽  
pp. 524-541
Author(s):  
J. Baumgartner ◽  
P. Erdös ◽  
F. Galvin ◽  
J. Larson
Keyword(s):  
Complete Graph ◽  
Edge Coloring ◽  
Cardinal Numbers ◽  
Symmetrizable Space ◽  
Element Set

Use the two element subsets of κ, denoted by [κ]2, as the edge set for the complete graph on κ points. Write CP(κ, µ, v) if there is an edge coloring R: [κ]2 → µ with µ colors so that for every proper v element set X ⊊ κ, there is a point x ∈ κ ∼ X so that the edges between x and X receive at least the minimum of µ and v colors. Write CP⧣(K, µ, v) if the coloring is oneto- one on the edges between x and elements of X.Peter W. Harley III [5] introduced CP and proved that for κ ≧ ω, CP(κ+, κ, κ) holds to solve a topological problem, since the fact that CP(ℵ1, ℵ0, ℵ0) holds implies the existence of a symmetrizable space on ℵ1 points in which no point is a Gδ.

scholarly journals A natural representation of partitions as terms of a universal algebra

1993 ◽  
Vol 55 (3) ◽  
pp. 311-324
Author(s):  
Harry Lakser
Keyword(s):  
Universal Algebra ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Variety Of Algebras ◽  
Natural Representation ◽  
Necessary And Sufficient ◽  
Element Set

AbstractWe consider a variety of algebras with two binary commutative and associative operations. For each integer n ≥ 0, we represent the partitions on an n-element set as n-ary terms in the variety. We determine necessary and sufficient conditions on the variety ensuring that, for each n, these representing terms be all the essentially n-ary terms and moreover that distinct partitions yield distinct terms.

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