Evacuation of labelled graphs
نویسندگان
چکیده
In this note, we extend Schiitzenberger’s evacuation of Young tableaux (Schtitzenberger, 1963), and naturally labelled posets (Schltzenberger, 1972), to labelled graphs. It is shown that evacuation is an involution, and that in that in the dual evacuation, tracks and trajectories are interchanged. Let G = ( V, E) be a simple undirected graph without loops; V is its set of vertices, and E its set of edges, with E sP2( V). A labelling of G is a bijective map @: T/+(1, . ..) n), with n=(V(. The (canonical) track P(Q) of @ is the subset {ol, . . . . uk} of V with: (i) v,=@-‘(l); (ii) for i >, 2, vi = @‘(min{ Q(v) ( (u, vi _ 1)~ E and Q(u) > ~(Vi_ ,)I) if such a vector Vi exists; (iii) if such Ui does not exist, then k= i1. The promotion of @ is the mapping a:@-+a@ defined by: &P(u)= Q(u)1 if u+!P(@), a~(vi)=~(Ui+,)-l for i=l,...,k-1, &D(Vk)=n. (1) Example. Consider (G, @) as in Fig. 1. The track is the set of circled vertices. The promotion of @ is shown in Fig. 2. With @ as above and SE{ 1,. _. , n>, the s-promotion of @ is the mapping 8,: @+a,@ obtained by the previous construction restricted to the vertices labelled in { 1, . . . , .s} *Supported by a CRSNG grant (Canada). *Corresponding author. 0012-365X/94/$07.00
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عنوان ژورنال:
- Discrete Mathematics
دوره 132 شماره
صفحات -
تاریخ انتشار 1994