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Showing 1 to 4 of 4 for “"young diagram"”.
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Pattern-avoidance in binary fillings of grid shapes
… is a set of boxes chosen from a square grid; any Young diagram is an example. We consider a notion of pattern-avoidance for 0-1 fillings of grid shapes, which generalizes permutation pattern-avoidance. A filling avoids a set of patterns if none of its sub-shapes, obtained by removing some rows and …
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Combinatorics of colored factorizations, flow polytopes and of matrices over finite fields
… we show that when the set of entries is a skew Young diagram, the numbers, up to a power of q - 1, are polynomials with nonnegative coefficients. We apply this result to the case when the set of entries is the Rothe diagram of a permutation. We end by giving conjectures connecting invertible …
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Behavior of partition values modulo powers of primes
… if none of the hook lengths in the Ferrers-Young diagram are divisible by <italic>t</italic>. We prove a wealth of new congruences for <italic>2<super>t</super></italic>-core partitions modulo 2 by examining the nilpotency of Hecke operators on level 1 cusp forms. Based on extensive …
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Matrix Representations of Automorphism Groups of Free Groups
… subgroups is well understood in the language of Young Diagrams, and we apply this knowledge to better understand the representation theory of Aut (Fn). We also calculate irreducible representations of Aut (Fn) in low dimensions and for small n.