Hook type tableaux and partition identities
نویسندگان
چکیده
In this paper we exhibit the box-stacking principle (BSP) in conjunction with Young diagrams to prove generalizations of Stanley’s and Elder’s theorems without even use partition statistics general. We primarily focus on study theorem color context.
منابع مشابه
Partition Identities
A partition of a positive integer n (or a partition of weight n) is a non-decreasing sequence λ = (λ1, λ2, . . . , λk) of non-negative integers λi such that ∑k i=1 λi = n. The λi’s are the parts of the partition λ. Integer partitions are of particular interest in combinatorics, partly because many profound questions concerning integer partitions, solved and unsolved, are easily stated, but not ...
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We consider a generalization of the vicious walker model. Using a bijection map between the path configuration of the non-intersecting random walkers and the hook Young diagram, we compute the probability concerning the number of walker’s movements. Applying the saddle point method, we reveal that the scaling limit gives the Tracy–Widom distribution, which is same with the limit distribution of...
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Short, bijective proofs of identities for multisets of ‘hook pairs’ (arm-leg pairs) of the cells of certain diagrams are given. These hook pair identities were originally found by Regev.
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In this paper we find new classes of posets which generalize the d-complete posets. In fact the d-complete posets are classified into 15 irreducible classes in the paper “Dynkin diagram classification of λ-minuscule Bruhat lattices and of d-complete posets” (J. Algebraic Combin. 9 (1999), 61 – 94) by R. A. Proctor. Here we present six new classes of posets of hook-length property which generali...
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ژورنال
عنوان ژورنال: Notes on Number Theory and Discrete Mathematics
سال: 2022
ISSN: ['1310-5132', '2367-8275']
DOI: https://doi.org/10.7546/nntdm.2022.28.4.635-647