A Sign-reversing Involution for Rooted Special Rim-hook Tableaux
نویسنده
چکیده
Eg̃eciog̃lu and Remmel [2] gave an interpretation for the entries of the inverse Kostka matrix K in terms of special rim-hook tableaux. They were able to use this interpretation to give a combinatorial proof that KK = I but were unable to do the same for the equation KK = I. We define a sign-reversing involution on rooted special rim-hook tableaux which can be used to prove that the last column of this second product is correct. In addition, following a suggestion of Chow [1] we combine our involution with a result of Gasharov [5] to give a combinatorial proof of a special case of the (3+1)-free Conjecture of Stanley and Stembridge [14].
منابع مشابه
An algorithmic sign-reversing involution for special rim-hook tableaux
Eğecioğlu and Remmel [2] gave an interpretation for the entries of the inverse Kostka matrix K in terms of special rim-hook tableaux. They were able to use this interpretation to give a combinatorial proof that KK = I but were unable to do the same for the equation KK = I. We define an algorithmic signreversing involution on rooted special rim-hook tableaux which can be used to prove that the l...
متن کاملGeneralization of the Schensted Algorithm for Rim Hook Tableaux
In [6] Schensted constructed the Schensted algorithm, which gives a bijection between permutations and pairs of standard tableaux of the same shape. Stanton and White [8] gave analog of the Schensted algorithm for rim hook tableaux. In this paper we give a generalization of Stanton and White’s Schensted algorithm for rim hook tableaux. If k is a fixed positive integer, it shows a one-to-one cor...
متن کاملBipieri tableaux
We introduce a new class of combinatorial objects, which we call “bipieri tableaux,” which arise in a natural way from the evaluation of products consisting of commutative or noncommutative complete homogeneous symmetric functions and elementary symmetric functions through repeated applications of Pieri rules. We prove using sign-reversing involutions on bipieri tableaux an elegant coproduct fo...
متن کاملSwiching Rule on the Shifted Rim Hook Tableaux
When the Schur function sλ corresponding to a partition λ is defined as the generating function of the column strict tableaux of shape λ it is not at all obvious that sλ is symmetric. In [BK] Bender and Knuth showed that sλ is symmetric by describing a switching rule for column strict tableaux, which is essentially equivalent to the jeu de taquin of Schützenberger (see [Sü]). Bender and Knuth’s...
متن کاملAnother Involution Principle-Free Bijective Proof of Stanley's Hook-Content Formula
Another bijective proof of Stanley’s hook-content formula for the generating function for semistandard tableaux of a given shape is given that does not involve the involution principle of Garsia and Milne. It is the result of a merge of the modified jeu de taquin idea from the author’s previous bijective proof (“An involution principle-free bijective proof of Stanley’s hook-content formula”, Di...
متن کامل