poset


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poset

[′pō‚set]
(mathematics)

Pos’et

 

an urban-type settlement in Khasan Raion, Primor’e Krai, RSFSR. Pos’et is a port on Pos’et Bay of the Sea of Japan. There is a railroad station in the city. Pos’et has a fishing industry. The city was named in honor of the Russian navigator and admiral K. N. Pos’et (1819–89).

poset

References in periodicals archive ?
In a standard way, every poset can be considered as a category, and monotone mappings between posets can be considered as functors.
As a poset, it decomposes into levels, the levels of a poset P being defined inductively by the formula [P.
A subset A of a poset (S, [less than or equal to]) is said to be a down-set if s [member of] A whenever s [less than or equal to] a for s [member of] S, a [member of] A.
This allows us to compute these algebraic invariants using the combinatorics of the poset, which we do for certain classes of left regular bands in the next section.
A poset is called an (S, T)-biposet if it is a left Sand a right T-poset and its S- and T-actions commute with each other.
Then ( L, [less than or equal to]) is a poset and for any x, y [member of] L, x [conjunction] y is the inf{x, y} and x [disjunction] y the sup{x, y}.
We define the set of nonnesting partitions NN([PHI]) of [PHI] as the set of antichains in the root poset of [PHI].
Since dom g is a down-set in the poset [0, 1], also h(a) [member of] dom g, and hence a [member of] dom (gh).
Let P be a poset on [n] which is a sub-order of the usual total linear order.
We will now use the reverse composition poset to define standard reverse composition tableaux.
Recall the one-variable Mobius function of a poset, [mu]: P [right arrow] Z, is defined recursively by
However, O'Hara's construction does not give a symmetric chain decomposition of the poset L(l, m) of partitions which fit the l x m rectangle (in other words, the difference between successive partitions is not always a corner).