The MacNeille Completion of the Poset of Partial Injective Functions
نویسنده
چکیده
Abstract. Renner has defined an order on the set of partial injective functions from [n] = {1, . . . , n} to [n]. This order extends the Bruhat order on the symmetric group. The poset Pn obtained is isomorphic to a set of square matrices of size n with its natural order. We give the smallest lattice that contains Pn. This lattice is in bijection with the set of alternating matrices. These matrices generalize the classical alternating sign matrices. The set of join-irreducible elements of Pn are increasing functions for which the domain and the image are intervals.
منابع مشابه
Posets of Finite Functions
The symmetric group S(n) is partially ordered by Bruhat order. This order is extended by L. Renner to the set of partial injective functions of {1, 2, . . . , n} (see, Linear Algebraic Monoids, Springer, 2005). This poset is investigated by M. Fortin in his paper The MacNeille Completion of the Poset of Partial Injective Functions [Electron. J. Combin., 15, R62, 2008]. In this paper we show tha...
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عنوان ژورنال:
- Electr. J. Comb.
دوره 15 شماره
صفحات -
تاریخ انتشار 2008