Brief communication

Haglund, Lotta

doi:10.1111/j.1471-1842.2004.00470.x

Cited by 7 publications

(4 citation statements)

References 1 publication

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“…For the first equality, see for example [9]; for the second, see [5, equation (7)]. Corollary 3.5 was also discovered independently by James Haglund [3]. It is not difficult to prove it directly; in fact, it will be an immediate consequence of our next theorem.…”

Section: The Tutte Polynomialmentioning

confidence: 67%

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The Catalan matroid

Ardila

2003

Journal of Combinatorial Theory, Series A

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We show how the set of Dyck paths of length 2n naturally gives rise to a matroid, which we call the "Catalan matroid" C n . We describe this matroid in detail; among several other results, we show that C n is self-dual, it is representable over Q but not over finite fields F q with q ≤ n − 2, and it has a nice Tutte polynomial.We then generalize our construction to obtain a family of matroids, which we call "shifted matroids". They arose independently and almost simultaneously in the work of Klivans, who showed that they are precisely the matroids whose independence complex is a shifted complex.

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Section: The Tutte Polynomialmentioning

confidence: 67%

“…, λ k ) of n is a weakly decreasing sequence of positive integers which add up to n. We associate to it a Young diagram: a left-justified array of unit squares, which has λ i squares on the i-th row from top to bottom. 3 A standard Young tableaux is a placement of the integers 1, . .…”

Section: Shifted Matroidsmentioning

confidence: 99%

The Catalan matroid

Ardila

2003

Journal of Combinatorial Theory, Series A

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“…Mentoring is a process between two or more people that can be implemented in a variety of ways based on the needs and resources of the organization (Culpepper, 2000). Whether formal or informal processes are used, it is noteworthy to mention that mentoring can be a developmental strategy (Haglund, 2004;Murphy, 2008;Taylor, 1999), a tool for retention and promotion (Snow, 1990), or simply viewed as a process whereby there are stated or unstated benefits for the mentor, mentee, and the organization (Hardesty, 1997;Field, 2001;Munde, 2000). Though there are theoretical considerations for formal mentoring processes that include the ideas of social exchange and communitarianism (Gibb, 1999), this article offers more practical knowledge that mentoring practitioners may find beneficial in their daily interactions within academic libraries.…”

Section: Mentoring As Processmentioning

confidence: 99%

Purposeful Mentoring in Academic Libraries

Ross

2013

Journal of Library Administration

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This article offers statistical information about the future of our profession and the role that mentoring may play in retaining and promoting academic librarians into leadership positions within an organization. An overview of the history and definition of the word mentor and current terminology is offered to provide the reader with understanding of the complexity surrounding the concept of mentoring. Mentoring as process is explained, and both formal and informal mentoring processes are discussed and examples provided. The benefits of mentoring are detailed and include the benefits for mentors, mentees, and academic libraries, with a special focus on minorities and generational considerations now prevalent in libraries. Qualitative methodologies are examined to determine relationships, and the methods used include interviews, questionnaires, and print and online surveys. Case studies from across the nation are analyzed and offered as evidence that mentoring does in fact work well in many academic libraries, but librarians should be mindful that these mentoring processes must be evaluated periodically to remain viable. A brief discussion and future considerations section offer helpful information on gaps in the literature and the challenges that academic libraries face as they create and implement mentoring processes in their respective academic organizations.

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“…For example, we will show how (1) can be derived from Saalcshütz's identity. Jim Haglund [4] suggested that (1) should follow from Gasper's transformation [2] of hypergeometric series of Karlsson-Minton type. This is indeed the case but we will not include such a derivation in this paper since (1) is a special case of wider class of identities that arise by studying the problem of enumerating permutations according to the number of pattern matches where the equivalence classes of the elements modulo k for k ≥ 2 are taken into account, see [6].…”

Section: Introductionmentioning

confidence: 99%

Classifying Descents According to Equivalence mod k

Kitaev¹,

Remmel²

2006

Electron. J. Combin.

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In [5] the authors refine the well-known permutation statistic "descent" by fixing parity of (exactly) one of the descent's numbers. In this paper, we generalize the results of [5] by studying descents according to whether the first or the second element in a descent pair is equivalent to k mod k ≥ 2. We provide either an explicit or an inclusion-exclusion type formula for the distribution of the new statistics. Based on our results we obtain combinatorial proofs of a number of remarkable identities. We also provide bijective proofs of some of our results and state a number of open problems.

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Brief communication

Cited by 7 publications

References 1 publication

The Catalan matroid

The Catalan matroid

Purposeful Mentoring in Academic Libraries

Classifying Descents According to Equivalence mod k

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