Boolean elements in the Bruhat order on twisted involutions
نویسندگان
چکیده
منابع مشابه
Pattern avoidance and Boolean elements in the Bruhat order on involutions
We show that the principal order ideal of an element w in the Bruhat order on involutions in a symmetric group is a Boolean lattice if and only if w avoids the patterns 4321, 45312 and 456123. Similar criteria for signed permutations are also stated. Involutions with this property are enumerated with respect to natural statistics. In this context, a bijective correspondence with certain Motzkin...
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In this paper we study the partially ordered set of the involutions of the symmetric group Sn with the order induced by the Bruhat order of Sn . We prove that this is a graded poset, with rank function given by the average of the number of inversions and the number of excedances, and that it is lexicographically shellable, hence Cohen-Macaulay, and Eulerian.
متن کاملPattern Avoidance and the Bruhat Order on Involutions
We show that the principal order ideal below an element w in the Bruhat order on involutions in a symmetric group is a Boolean lattice if and only if w avoids the patterns 4321, 45312 and 456123. Similar criteria for signed permutations are also stated. Involutions with this property are enumerated with respect to natural statistics. In this context, a bijective correspondence with certain Motz...
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This thesis consists of two papers within two different areas of combinatorics. Ramsey theory is a classic topic in graph theory, and Paper A deals with two of its most fundamental problems: to compute Ramsey numbers and to characterise critical graphs. More precisely, we study generalised Ramsey numbers for two sets Γ1 and Γ2 of cycles. We determine, in particular, all generalised Ramsey numbe...
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Our purpose in this article is to investigate the order complex of inclusion poset PFn of Borel orbit closures in skew-symmetric matrices. We prove that PFn is an EL-shellable poset and furthermore its order complex triangulates a ball. We investigate (rook-theoretic) combinatorial properties of the rank-generating function of PFn in contrast with the zeta function of the variety of skew-symmet...
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ژورنال
عنوان ژورنال: Involve, a Journal of Mathematics
سال: 2012
ISSN: 1944-4184,1944-4176
DOI: 10.2140/involve.2012.5.339