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Your search keyword '"Mordechai Novick"' showing total 6 results
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6 results on '"Mordechai Novick"'

1. Depth in Coxeter groups of type $B$

Author

Eli Bagno, Riccardo Biagioli, and Mordechai Novick

Subjects
length, depths, reflections, coxeter groups, bruhat graph, [info.info-dm] computer science [cs]/discrete mathematics [cs.dm], Mathematics, QA1-939
Abstract

The depth statistic was defined for every Coxeter group in terms of factorizations of its elements into product of reflections. Essentially, the depth gives the minimal path cost in the Bruaht graph, where the edges have prescribed weights. We present an algorithm for calculating the depth of a signed permutation which yields a simple formula for this statistic. We use our algorithm to characterize signed permutations having depth equal to length. These are the fully commutative top-and-bottom elements defined by Stembridge. We finally give a characterization of the signed permutations in which the reflection length coincides with both the depth and the length.

Published
2015
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6. Depth in classical Coxeter groups

Author

Eli Bagno, Alexander Woo, Mordechai Novick, Riccardo Biagioli, Jerusalem College of Technology (JCT), Combinatoire, théorie des nombres (CTN), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Moscow Idaho], University of Idaho [Moscow, USA], Biagioli R, Bagno E, Novick M, and Woo A

Subjects
Discrete mathematics, Algebra and Number Theory, Coxeter notation, Length, Coxeter group, Depth, 010102 general mathematics, Reflection, 0102 computer and information sciences, Point group, 01 natural sciences, Bruhat order, Combinatorics, 010201 computation theory & mathematics, Coxeter complex, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], Bruhat graph, Discrete Mathematics and Combinatorics, Artin group, 0101 mathematics, Longest element of a Coxeter group, Coxeter element, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

The depth statistic was defined by Petersen and Tenner for an element of an arbitrary Coxeter group in terms of factorizations of the element into a product of reflections. It can also be defined as the minimal cost, given certain prescribed edge weights, for a path in the Bruhat graph from the identity to an element. We present algorithms for calculating the depth of an element of a classical Coxeter group that yield simple formulas for this statistic. We use our algorithms to characterize elements having depth equal to length. These are the short-braid-avoiding elements. We also give a characterization of the elements for which the reflection length coincides with both depth and length. These are the boolean elements.

Published
2016
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