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- W2028508093 abstract "Let P l , n denote the partition lattice of l with n parts, ordered by Hardy–Littlewood–Polya majorization. For any two comparable elements x and y of P l , n , we denote by M( x , y ) , m( x , y ) , f( x , y ) , and F( x , y ) , respectively, the sizes of four typical chains between x and y : the longest chain, the shortest chain, the lexicographic chain, and the counter-lexicographic chain. The covers u =(u 1 ,…,u n )≻ v =(v 1 ,…,v n ) in P l , n are of two types: N -shift (nearby shift) where v i = u i −1, v i +1 = u i +1 +1 for some i ; and D -shift (distant shift) where u i −1= v i = v i +1 =⋯= v j = u j +1 for some i and j . An N -shift (a D -shift) is pure if it is not a D -shift (an N -shift). We develop linear algorithms for calculating M( x , y ) , m( x , y ) , f( x , y ) , and F( x , y ) , using the leftmost pure N -shift first search, the rightmost pure D -shift first search, the leftmost N -shift first search, and the rightmost D -shift first search, respectively. Those algorithms have significant applications in complexity analysis of biological sequences." @default.
- W2028508093 created "2016-06-24" @default.
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- W2028508093 date "2002-10-01" @default.
- W2028508093 modified "2023-09-26" @default.
- W2028508093 title "Algorithms for computing lengths of chains in integral partition lattices" @default.
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- W2028508093 doi "https://doi.org/10.1016/s0304-3975(01)00392-9" @default.
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