ترغب بنشر مسار تعليمي؟ اضغط هنا

Mitschs order and inclusion for binary relations and partitions

36   0   0.0 ( 0 )
 نشر من قبل Desmond FitzGerald
 تاريخ النشر 2012
  مجال البحث
والبحث باللغة English
 تأليف D. G. FitzGerald




اسأل ChatGPT حول البحث

Mitschs natural partial order on the semigroup of binary relations is here characterised by equations in the theory of relation algebras. The natural partial order has a complex relationship with the compatible partial order of inclusion, which is explored by means of a sublattice of the lattice of preorders on the semigroup. The corresponding sublattice for the partition monoid is also described.

قيم البحث

اقرأ أيضاً

Let $G$ be a nonabelian group, $Asubseteq G$ an abelian subgroup and $ngeqslant 2$ an integer. We say that $G$ has an $n$-abelian partition with respect to $A$, if there exists a partition of $G$ into $A$ and $n$ disjoint commuting subsets $A_1, A_2, ldots, A_n$ of $G$, such that $|A_i|>1$ for each $i=1, 2, ldots, n$. We first classify all nonabelian groups, up to isomorphism, which have an $n$-abelian partition for $n=2, 3$. Then, we provide some formulas concerning the number of spanning trees of commuting graphs associated with certain finite groups. Finally, we point out some ways to finding the number of spanning trees of the commuting graphs of some specific groups.
A binary relation on a finite set is called a Hall relation if it contains a permutation of the set. Under the usual relational product, Hall relations form a semigroup which is known to be a block-group, that is, a semigroup with at most one idempot ent in each $mathrsfs{R}$-class and each $mathrsfs{L}$-class. Here we show that in a certain sense, the converse is true: every block-group divides a semigroup of Hall relations on a finite set.
111 - O. Dovgoshey 2019
Let $X$ be a nonempty set and $X^{2}$ be the Cartesian square of $X$. Some semigroups of binary relations generated partitions of $X^2$ are studied. In particular, the algebraic structure of semigroups generated by the finest partition of $X^{2}$ and , respectively, by the finest symmetric partition of $X^{2}$ are described.
In this paper, we establish the sharp conditions for the inclusion relations between Besov spaces $B_{p,q}$ and Wiener amalgam spaces $W_{p,q}^s$. We also obtain the optimal inclusion relations between local hardy spaces $h^p$ and Wiener amalgam spac es $W_{p,q}^s$, which completely improve and extend the main results obtained by Cunanana, Kobayashib and Sugimotoa in [J. Funct. Anal. 268 (2015), 239-254]. In addition, we establish some mild characterizations of inclusion relations between Triebel-Lizorkin and Wiener amalgam spaces, which relates some modern inequalities to classical inequalities.
In this paper we demonstrate connections between three seemingly unrelated concepts. (1) The discrete isoperimetric problem in the infinite binary tree with all the leaves at the same level, $ {mathcal T}_{infty}$: The $n$-th edge isoperimetric n umber $delta(n)$ is defined to be $min_{|S|=n, S subset V({mathcal T}_{infty})} |(S,bar{S})|$, where $(S,bar{S})$ is the set of edges in the cut defined by $S$. (2) Signed almost binary partitions: This is the special case of the coin-changing problem where the coins are drawn from the set ${pm (2^d - 1): $d$ is a positive integer}$. The quantity of interest is $tau(n)$, the minimum number of coins necessary to make change for $n$ cents. (3) Certain Meta-Fibonacci sequences: The Tanny sequence is defined by $T(n)=T(n{-}1{-}T(n{-}1))+T(n{-}2{-}T(n{-}2))$ and the Conolly sequence is defined by $C(n)=C(n{-}C(n{-}1))+C(n{-}1{-}C(n{-}2))$, where the initial conditions are $T(1) = C(1) = T(2) = C(2) = 1$. These are well-known meta-Fibonacci sequences. The main result that ties these three together is the following: $$ delta(n) = tau(n) = n+ 2 + 2 min_{1 le k le n} (C(k) - T(n-k) - k).$$ Apart from this, we prove several other results which bring out the interconnections between the above three concepts.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا