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On quotients of posets, with an application to the q-analog of the hypercube

DSpace at IIT Bombay

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Title On quotients of posets, with an application to the q-analog of the hypercube
 
Creator SRINIVASAN, MK
 
Subject geometry
theorem
chains
order
sperner theory
group actions
quotients of posets
fixed points
 
Description Let G be a finite group having an order preserving and rank preserving action on a finite ranked poset P. Let P/G denote the quotient poset. A well known result in algebraic Sperner theory asserts that an order raising G-linear map on V(P) (the complex vector space with P as basis) satisfying the full rank property induces an order raising linear map on V(P/G), also satisfying the full rank property. In this paper we prove a kind of converse result that has applications to Boolean algebras and their cubical and q-analogs. For a finite ranked poset P, let L denote the Lefschetz order raising map taking an element to the sum of the elements covering it and let P-i, 0 less than or equal to i less than or equal to n, where n = rank(P), denote the set of elements of rank i. We say that P is unitary Peck (respectively, unitary semi-Peck) if the map Ln-2i : V(P-i) --> V(Pn-i), i < n/2 is bijective (respectively, injective). We show that the q-analog of the n-cube is unitary semi-Peck. (C) 2003
 
Publisher ACADEMIC PRESS LTD ELSEVIER SCIENCE LTD
 
Date 2011-07-12T20:31:07Z
2011-12-26T13:02:51Z
2011-12-27T05:50:06Z
2011-07-12T20:31:07Z
2011-12-26T13:02:51Z
2011-12-27T05:50:06Z
2004
 
Type Article
 
Identifier EUROPEAN JOURNAL OF COMBINATORICS, 25(5), 675-683
0195-6698
http://dx.doi.org/10.1016/j.ejc.2003.09.015
http://dspace.library.iitb.ac.in/xmlui/handle/10054/3584
http://hdl.handle.net/10054/3584
 
Language en